LAGGED EFFECTS OF MONETARY GROWTH RATES ON INTEREST RATES by MATHIAS ETTA EGBE, B.A., M.S.B.A., M.A A DISSERTATION IN ECONOMICS Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Approved í/ Accepted Dean of the Graduate School December, 1984
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LAGGED EFFECTS OF MONETARY GROWTH RATES ON INTEREST RATES
by
MATHIAS ETTA EGBE, B.A., M.S.B.A., M.A
A DISSERTATION
IN
ECONOMICS
Submitted to the Graduate Faculty of Texas Tech University in
Partial Fulfillment of the Requirements for
the Degree of
DOCTOR OF PHILOSOPHY
Approved
í/ Accepted
Dean of the Graduate School
December, 1984
' ' 'Y ' ACKNOWLEDGMENTS
I wish to thank Dr. Ronald D. Gilbert for his patience
and guidance throughout this research. My appreciation is
also extended to the other committee members, Dr. Lewis E.
Hill and Dr. Robert L. Rouse. I also wish to express my
thanks to Dr. Sujit K. Roy for his guidance and especially
in his efforts in securing the Shazam software used for the
study. I would also like to extend my gratitude to the Eco-
nomics department, the Government of the Republic of Came-
roon and Texas Instruments Inc. for providing financial as-
sistance during my undergraduate and graduate studies.
Special appreciation is extended to my wife, Valerie,
for typing the tables and figures and also for the sacrific-
es she made in our family iife. I would also like to thank
Mr. Wendell Broom for his editorial services.
11
CONTENTS
ACKNOWLEDGMENTS
CHAPTER
I. INTRODUCTION
Statement of the Problem Objectives General Procedures
Uniqueness of Study From Past Studies
II. REVIEW OF LITERATURE
Summary of Literature
III. CONCEPTUAL FRAMEWORK
Survey Of Theoretical Underpinnings An Economy without any Exchange Opportunities Production and Consumption Takes Place in One
Time Period Time Preferences and Investment Opportunities Lending, Borrowing, and Time Preferences Interest Rate Determination Using Credit Mar-
ket Theory and the Edgeworth Exchange Box
Loanable Funds Theory of Interest Rate Sources of Supply and Demand of Loanable-
Funds Liquidity-Preference Theory of Interest Rate The Equivalence of the Liquidity Prefence and
Loanable-Funds Theories of Interest The Various Effects of a Monetary Growth
Disturbance on the Nominal Interest Rate The Liquidity Effect The Income Effect The Fisher or Inflationary Expectations
Effect The Financial Effect
Exposure of Hypothetical Model Role of the Rate of Interest in an Economy
111
IV. METHOD AND PROCEDURES 7 2
Basic Data and Definitions 73 United States Data 73
Money 73 Interest Rates 74
United Kingdom Data 75 Money 7 5 Interest Rate 75
Federal Republic of Germany Data 76 Money 76 Interest Rate 76 An Overview of Institutional Arrangements for
Monetary Control within the Three Coun-tries of the Study 77
Specification of Methods and Procedures 79 Other Procedures 85 Brief Outline of the Chow Test 86 Brief Outline of the Dummy Variable Test 88
V. RESULTS AND ANALYSIS 91
Segmentation of Time Period 91 United States 91
Adjusted Monthly Observations 91 Key to Table Notations and Definitions of
Estimation Results for Quarterly M3 I/1969-IV/1980 164
Revised Estimation of Equation on SAMl 1978-1980 166
Simulation Results 171
VI. SUMMARY AND CONCLUSION 17 9
Summary of Results 182 Conclusion 185
REFERENCES 191
APPENDIX
A. SOURCES OF DATA FOR THE MONETARY MEASURES AND THE TREASURY BILL RATE 201
B. DATA OF MONETARY STOCK MEASURES AND THE 3 MONTH TREASURY BILL RATE FOR THE UNITED STATES 202
C. DATA OF MONETARY STOCK MEASURES AND THE 3 MONTH TREASURY BILL RATE FOR THE UNITED KINGDOM 215
D. DATA OF MONETARY STOCK MEASURES AND THE 3 MONTH TREASURY BILL RATE FOR THE FEDERAL REPUBLIC OF GERMANY 22 3
VI
LIST OF TABLES
1. Summary of Structural Test for U.S. Data 92
2. Summary of Structural Test for U.K. Data 96
3. Summary of Structural Test for F.G.R Data 99
4. Average Annual Growth Rate of Ml, and Inflation Rate, and Short-Term Treasury bill Rate 102
5. Annual Rate of Change in Money and Prices in Six
Industrial Nations 1971-1977 105
6. United States Monthly Regression Results for Ml- 107
7. United States Monthly Regression Results for M2 111
8. United States Monthly Regression Results for M3 114
9. United States Monthly Regression Results for L 115
10. United States Quarterly Regression Results for Ml 117
11. United States Quarterly Regression Results for M2 122
12. United States Quarterly Regression Results for M3 125
13. United States Quarterly Regression Results for L 128
14. United Kingdom Monthly Regression Results for Ml 131
15. United Kingdom Monthly Regression Results for M2 134
16. United Kingdom Monthly Regression Results for M3 137
17. United Kingdom Quarterly Regression Results for Ml 140
18. United Kingdom Quarterly Regression Results for M2 143
19. United Kingdom Quarterly Regression Results for M3 145
20. West Germany Monthly Regression Results for Ml 148 21. West Germany Monthly Regression Results for M2 152
VI 1
22. West Germany Monthly Regression Results for M3 155
23. West Germany Quarterly Regression Results for Ml 159
24. West Germany Quarterly Regression Results for M2 162
25. West Germany Quarterly Regression Results for M3 165
26. United Kingdom Regression Results for SAMl 1978-1980 167
27. West Germany Regression Results for SAMl 1978-1980 168
28. United States Regression Results for SAMl 1978-1980 170
29. United States Full In-Sample Simulation And Post-Sam-ple Forecast Summary Statistics On Monthly SAMl 1978-1980 172
30. United Kingdom Full In-Sample Simulation And Post-Sample Forecast Summary Statistics On Monthly SAMl 1978-1980 172
31. West Germany Full In-Sample Simulation And Post-Sam-ple Forecast Summary Statistics On Monthly SAMl 1978-1980 173
32. United States Full In-Sample Simulation And Post-Sam-ple Forecast Summary Statistics On Quarterly SAMl 174
33. United Kingdom Full In-Sample Simulation And Post-Sample Forecast Summary Statistics On Quarterly SAMl 175
34. West Germany Full In-Sample Simulation And Post-Sam-ple Forecast Summary Statistics On Quarterly SAMl 175
VI 1 1
LIST OF FIGURES
1. Determination of the Interest Rate 46
2. Interest Rate Determination in the Credit Market 51
3. Equilibrium in the Credit Market 54
4. Equilibrium in the Money Market 59
5. Hypothetical Model 68
IX
CHAPTER I
INTRODUCTION
Statement of the Problem
A widely held view is that changes in the monetary
growth rate operate on the nominal interest rate-'- through
systematically lagged liquidity, income, and Fisher effects.
It is also widely believed that market interest rates follow
a particular time path in response to the changes in the
rate of monetary growth. This time path is important be-
cause interest rates are thought to be one of the conduits
of monetary policy.
The length of the time path followed by interest rate
reveals information concerning the lag in monetary policy's
effect. Curiosity about this time path provided the initial
motivation for earlier empirical invest igations.' After
such a general introduction on the nature of lags, their im-
•'• The rate of interest referred to henceforth is the nominal interest rate, unless otherwise specifically stated, since the demand and supply conditions in the market determines only the nominal interest rate. Moreover according to Rob-ert A. Mundell (1963), the rate of interest relevant for de-cisions regarding the allocation of wealth between money and other assets is the nominal rate.
^ Some examples of such investigations are those carried out by Phillip Cagan (1972); P. Cagan and A. Gandolfi (1969); William Gibson (1970a, 1070b, 1972); William Gibson and E. Kaufman (1968).
2
plications for monetary policy, and their effects on nominal
interest rate movement, let us turn to the specifics about
interest rates.
The major bifurcation of the more modern and advanced
theories of the determination of interest rates is between
the following two categories:
(1) Those based on the neoclassical loanable funds
theory which was earliest advanced by Leon Walras
(1900) in a general equilibrium framework, in con-
trast to the partial equilibrium approach advanced
by other neoclassicists, with Knut Wicksell (1954)
and Irving Fisher (1930) inclusive.
(2) Those based on the liquidity preference theory,
earliest advanced by Lord John Maynard Keynes
(1936).
Preceding the modern theories, however, were classical
theories pioneered by such early writers as Von Bohm-Bawerk
(1956). This study will address the neoclassical theories
of the determination of interest rates, specifically the an-
alytical separation of monetary policy effects on interest
rates into liquidity, income, inflationary expectations and
financial effects.
The basis for the neoclassical loanable-funds theory is
the notion that the real interest rate is determined by the
flow of funds supplied and demanded. It implies that "real"
interest rate will be in equilibrium when it is at a level
which equates the demand for and the supply of "loanable
funds." Fisher's (1930) pure form of the nonmonetary loana-
ble-funds theory was stated in terms of desired lending and
desired borrowing. It was this (Fisher's) nonmonetary ap-
proach that Keynes (1936) attacked as the "classical" theory
of interest.
The liquidity preference theory focuses on the supply
of and demand for money. It analyzes the nominal interest
rate in terms of money stock supplied and demanded in con-
trast to the loanable-funds theory, which does so in terms
of the flow of changes in the money stock. In addition, the
loanable-funds theory determines only the "real" interest
rate.
There is a considerable body of literature concerned
with the problem of whether these differences are substan-
tial or whether the loanable funds and the liquidity prefer-
ence theories are fundamentally identical. The fact of the
matter is that the formal equivalence of liquidity prefer-
ence and monetary loanable funds theories depends on the
model builder's vision of the world. If the rate of
interest is determined by simultaneous equilibrium in all
the market, then it is of no consequence whether we ignore
the bond market or the money market even if both money and
bonds are traded on stock and flow markets (Hicks 1967).
Also the fact that one model is framed in terms of stocks
and the other in terms of flows is an insignificant distinc-
tion if we assume that the stock model refers to end-of-
period stocks when time is divided into discrete periods
(Patinkin 1959).
Michael R. Darby (1975) argued that "standard analysis
of monetary policy effects on interest rates in terms of li-
quidity, income and inflationary expectations is incom-
plete," because it omits the financial and tax effects.
Darby's argument was that after a change in monetary policy,
substitution among securities will increase as time elapses
and so reduce or eliminate financial effects caused by
short-run financial market segmentation. Another argument
was that the standard expectations effect omits the transfer
of income tax liability on that part of the interest payment
Hence, if the expected rate of inflation goes up by one per-
centage point, the nominal interest rate must increase by
enough to cover not only the loss of principal due to infla-
tion, but also by enough to pay the taxes on that return of
principal, that is by 1 / (1-t) percentage points, t being
the marginal tax rate.
Professor Milton Friedman (1968b) in his presidential
address to the eightieth annual meeting of the American
Economic Association, emphasized the many "misunderstood"
features of the relation between money stock and interest
rates. He also mentioned the inability of the Federal Re-
serve System to control interest rates, and hailed the aban-
donment of the Federal Reserve policy of pegging bond prices
as "a desirable and inevitable step." Friedman argued that
as an empirical matter, low interest rates are a sign that
monetary policy has been "tight," in the sense that the
quantity of money has grown slowly. And high interest rates
are a sign that the quantity of money has grown rapidly.
Paul Volcker while Chairman of the Federal Reserve System
had once supported this view in his speech.^ The broadest
fact of experience runs in precisely the opposite direction
from that which the financial community and the academic
economists have taken for granted. Phillip Cagan (1972,
• See Economic Review Federal Reserve Bank of Atlanta, Sep-tember 1981, pp. 22-25. 1981 Monetary Policy: Excerpts from testimony by the Federal Reserve Chairman, Paul A. Volcker before the House Banking Committee July 2, 1981, where the chairman says
Indeed sustained monetary restraint, by encourag-ing greater confidence in the price outlook, will in time bring interest rates lower.
Also William P. Yohe and Denis S. Karnosky in 1969 wrote
High interest rates do not necessarily indicate monetary restrain. Instead, they most likely in-dicate excessive monetary ease (as measured by rapid expansion of the money supply) which results in rapid total spending and eventually inflation.
6
1969) once voiced his surprise at one of the oldest tenets
of Wall Street: that "tight" monetary policy increases the
level of interest rates and "easy" monetary policy reduces
them. Gibson (1972a) acknowledges that the monetary author-
ity had not been able to control interest rates, because to
assure low nominal interest rates they would have to start
out in what seems to be the opposite direction, that is by
engaging in a deflationary monetary policy. And similarly
to assure high interest rates, they would have to start by
engaging in an inflationary monetary policy, accepting a
temporary movement in interest rates in the opposite direc-
tion.
Here are a few notable quotations on this yet-to-be-
settled issue.
During this period, monetary growth being comparatively slow, commercial banks had to bid aggressively for additional funds, resulting in very rapid time deposit growth. In contrast from July through November 1982, business loan demand slowed, monetary growth accelerated and interest rates declined sharply (Mack Ott, 1982, pp. 1-2).
It is commonly argued that interest rates and the growth rate of money (Ml) are negatively re-lated (and this we find in many text books); how-ever, data since late 1981 indicate that this has not been the case.... From the four weeks ending November 18, 1981 to the four weeks ending February 24, 1982, Ml grew at nearly 11 percent rate, yet short-term rates increased substantially. Similarly , money growth has slowed since late February, while short-term interest rates have trended downward (U.S. Financial Data, Federal Reserve Bank of St. Louis, 1982 pp. 1-2).
It is commonly argued that, all other things equal, an increase in the rate of money growth leads to lower interest rates while a decrease leads to higher interest rates. This short-term or "liquidity" effect generally is short-lived, however as evidence ... The dramatic increase in the rate of Ml growth beginning in November 1981 initially was accompanied by 250-300 basis points decline in short-term interest rates. As this ac-celerated money growth continued for the next two months, however, short-term rates rose (Dallas S. Batten, 1983, pp. 1-2).
The most abrupt decline in interest rates oc-cured in the face of sharply rising estimates of Federal Government budget deficits and during a period of relatively modest monetary growth. In-terest rates were roughly unchanged during the last four months of 1982 even though this period was characterized by very rapid monetary growth (Gary Santoni, 1983, pp. 1-2).
For whilst an increase in the quantity of money may be expected, cet. par. to reduce the rate of interest, this will not happen if the li-quidity preferences of the public are increasing more than the quantity of money (John Maynard Keynes, 1936, pp. 173).
It therefore appears that recent empirical observations
point to the fact that an inverse relationship between the
growth rate of the quantity of money and the interest rate
cannot be taken for granted any longer. There are indica-
tions of a possible positive relationship and if that is the
case, then to lower interest rates, the monetary authority
would have to decelerate the growth rate of the quantity of
money, and to assure higher interest rates they will have to
accelerate the growth rate of the quantity of money, ceteris
paribus.
8
Lawrence T. Clark (1981) argued that "the most
controversial issue in monetary policy today is the time lag
that occurs between a change in the money stock and its ef-
fects on the gross national product." He further argued
that the empirical studies on the effects of monetary policy
have failed to be convincing. These empirical studies have
been controversial and may have failed to be convincing for
a number of reasons:
(1) The theoretical model refers to an interest rate
that is an index of the interest rate on a variety
of loans, but empirical studies have almost exclu-
sively used interest rates on highly liquid bonds.
(2) Omission of the Financial and Tax effects in earli-
er analysis.
(3) Arbitrary selection of monetary variables; for in-
stance using Ml rather than M2, monetary base or
excess reserves.
(4) Differences in the estimation or econometric models
used in the analysis.
For these reasons, Clark (1981) concluded in 1981 that more
research work is needed in this area.
Objectives
The main objective of this study is to analyze statis-
tically the hypothesis that a rapid growth of the money
stock will lower interest rates, whereas a slow growth will
mean higher interest rates.
The secondary objectives of the study are
(A) Analyze the effects of the variability of the money
stock growth rate from trend or any reference point
on the market interest rates.
(B) A structural test of the model within the main ob-
jective to investigate any institutional or struc-
tural changes in the model.
(C) A comparative analysis of the mean length of lag
within similar periods among three major industrial
countries:
(1) The United States,
(2) The United Kingdom, and
(3) The Federal Republic of Germany.
For the comparative analysis, we looked at such indica-
tors as monetary policy, size of government deficits over
the years, the financial as well as the institutional
system, and the credit and the money market regulations
enforced by the respective central banking bodies.
10
General Procedures
The basic analytical tool used to satisfy the stated
main objective was the Almon polynomial distributed lag mod-
el. The regressor variable was the distributed lag first
difference of the log of the money stock, and the dependent
variable was the first difference of the log of the short-
term Treasury bill rate. The change in the log of the abso-
lute value of the money stock between successive periods
(that is the first difference) was used as a proxy variable
for the growth rate of the money stock.
The verification for any change in the structure was
carried out using both the Chow test and the dummy variable
test.
Uniqueness of Study From Past Studies
1. This research provided an opportunity in which a
comparative analysis across major advanced capital-
ist nations was carried out, as far as the relation-
ship between the growth rate of the money stock and
the market interest rate is concerned.
^ The Chow test is that described by Gregory C. Chow (1960). And the dummy variable test is that described by Damodar Gu-jar (1970a, 1970b).
11
2. Besides, the analysis across these countries was
done using all measures of monetary aggregates, Ml,
M2, M3, and L. Most past studies have used one
measure of monetary aggregate or another, and in
about 80 percent of the cases, adjusted Ml had been
used. Many other studies have used the inflationary
expectations, which is normally a distributed lag of
past inflations. The relationship was examined in
this study using all known measures of monetary ag-
gregates. Also both the seasonally adjusted and the
seasonally unadjusted data were covered in this
study.
A preview of the various parts of this study is appro-
priate at this point. The present chapter covers the intro-
ductory material on the statement of the problem, the basic
objectives of the study, and the general procedures used to
achieved these objectives. Chapter II is a selective review
of literature related to this study. The focus of Chapter
III is the conceptual framework, and the topics discussed
are the theoretical underpinnings of the rate of interest,
the determination of the rate of interest in the credit
market, and the role of the rate of interest in an economy,
as well as an exposition of the hypothetical model used for
the research. Chapter IV deals with the specification of
the methods and procedures used, the basic data used, and
12
the definitions of monetary aggregates for the various
countries. Also covered in this chapter is an overview of
the institutional arrangements for monetary controi within
the countries in the study. Chapter V covers the results of
the research, an analysis of the results, and comparison of
these results to previous studies. Chapter VI contains a
summary of the results, an assertion of the contribution of
this research to the literature and any implications from
the results obtained.
CHAPTER II
REVIEW OF LITERATURE
It is appropriate to start the review of literature
with Irving Fisher (1930), whose price expectation theory
dates as far back as 1896 but for some reasons was ignored
by most Economists for several decades despite the mass of
evidence Fisher presented. However, the price expectation
theory has been revived in the past decade or two due proba-
bly to the substantial price changes within this period.
According to Fisher, the price expectations effect raises
the nominal rate by exactly the expected rate of the price
increase. The real rate remains unchanged. In equation
form, Fisher's effect is written as follows: (1 -»• R') = (1 -•-
R) (1 + P*) where l-^R' =l-t-R-t-P*-i- RP*; which implies
R' = R -H P* + RP*, where
R' is the nominal rate,
R is the real rate,
P* is the expected price change,
and RP* is the cross product.
Robert A. Mundell (1963), prodded by Fisher's
reservations concerning the actual price expectations effect
on the nominal rate, developed a model which "showed that
anticipated inflation or deflation is likely to raise or
13
14
lower the nominal or money rate of interest by less than the
expected rate of inflation or deflation because the real
rate does not remain unchanged." AR < ---P*
Mundell's argument is based on the fact that inflation
reduces real money balances, and that the resulting decline
in wealth stimulates increased saving. He reasoned that
foreseeable fluctuations in the rate of inflation can have
real effects on economic activity. When prices are expected
to rise, the money rate of interest rises by less than the
rate of inflation, giving impetus to an investment boom and
an acceleration of growth. Conversely when a rise in prices
is expected to end, there occurs a stock market slump, a
rise in the real rate of interest, and a deceleration of
growth.
However, Frank G. Steindl (1973) asserted that the ef-
fect of anticipated inflation on real rate cannot be deter-
mined a priori, and that the real rate rises if the de-
creased real demand for money primarily finances increased
real commodity demand and falls if real bond demands are the
principal beneficiary.
But Michael R. Darby (1975, 1976) theoretically argued
that, due to tax considerations, the nominal interest rate
will always rise more than or fall less than the anticipated
increase in prices. A rise is needed simply to pay for the
additional tax that is expected to be paid. A decrease for
15
deflationary price expectations to take account of the fact
that the investor's marginal tax rate will decrease due to a
decline in income. The higher the marginal tax rate of the
1 AP''
investor, the greater the change in the nominal rate. AR> —-P"
J. M. Keynes' (1936) liquidity preference theory, basi-
cally states that the market interest rate is determined
fundamentally by the supply of and demand for money, and
that an increase in the money stock will lower the market
interest rate and a decrease will raise the rate.
Thomas Sargent (1972) combined the Fisherian analysis
with a loanable funds model of the determination of the real
interest rate. By positing that investment is a function of
the real interest rates and the current annual change in
GNP, and that savings is a function of the real interest
rate and the level of GNP, Sargent expressed the equilibrium
real rate as a function of the level and change in GNP.
Martin Feldstein and Otto Eckstein (1970) combined the
Fisherian price expectation theory to the liquidity prefer-
ence model. Their complete model is as follows:
RC^= a- + a,Log(N ) + a_Log(YJ +a_Log(RC -RC^ ,) + ? a,P* t U l t Z t j t t-i 4=] 4 j
where M is the real per capita monetary base,
Y is the real per capita gross national product.
16
D is the real per capita government debt held by
the public,
P* is the price expectation, and
RC is the interest rate on Moody's seasoned cor-
porate AAA bonds.
The monetary base, the national product and the govern-
ment debt were used as proxy variables for the real rate. A
third-degree Almon distributed lag of past inflations was
used as a proxy variable for the price expectation. Feld-
stein and Eckstein concluded that a combination of a static
liquidity preference model and an expected inflation adjust-
ment provide an extremely good explanation of the variation
in the corporate bond interest, and also that inflation had
been the dominant force in causing the rise in interest
rates since 1965.
Yohe and Karnosky (1969), in another study, sought to
explain the fluctuations in nominal interest rate (R) solely
in terms of the variation of price expectations (P*). They
assumed that the variance of nominal interest rate is due
primarily to the variance in price expectations, and that
the variety of forces which may shock interest rates are
orthogonal to their distributed lag proxies for inflationary
expectations.
17
Yohe and Karnosky's model is as follows:
where U is the disturbance term.
Unlike earlier studies, this study showed that price
level changes since 1952 have evidently come to have a
prompt and substantial effect on price expectations and nom-
inal interest rates. This study also showed that the total
effect of price expectations on interest rates and the speed
at which they are formed appeared to have increased since
1960. Most significantly was the finding that price level
rather than "real" rates accounts for nearly all the varia-
tion in nominal interest rates since 1961. The implied
speed of response in this study was much greater than that
of Feldstein and Eckstein's study.
Jack Carr and Lawrence B. Smith (1972), in another
study, attempted to synthesize two monetary forces which af-
fect interest rates. In the spirit of Wicksell, Carr and
Smith constructed a variable to measure the difference be-
tween actual (M) and expected (M*) rate of growth of the
money supply. An increase (decrease) in the unanticipated
rate of growth of the money supply is hypothesized to lower
(raise) interest rates. The second channel by which
monetary forces influence nominal interest rate is through
18
the Fisher effect, with changes in the money supply
affecting the actual and ultimately the expected rate of in-
flation. Carr and Smith used this model:
\ = ao+a^ (M -M*_^) + a^ J^ P % U_
where U as before is the disturbance term.
Jenkins and Lim (1973) in their own study reflected the
belief that the real interest rate evolves very slowly over
time and that the variance of the nominal rate primarily
reflects the variance of price expectations. The real rate
can be shocked both by monetary policy and by the rate of
growth of the total government debt held by the general pub-
lic. The model used by Jenkins and Lim is as follows:
^ = "0 + Jo «1 («t-l - "t-l-l' ilo Vt ^ "3^* + 't
In another study, William E. Gibson and George G. Kauf-
man (1968a, 1968b) set out to determine if short-run changes
in post war interest rates primarily reflects changes in the
demand for funds or changes in the supply of funds. Short-
term interest rates were regressed on industrial output and
on one of the measures of the money supply.
In other studies, William E. Gibson (1972, 1970a)
concluded that a change in the money stock produces an
19
immediate negative effect on interest rates, but only a
little later positive effects which tended to offset the
initial negative effects. The functional relation used by
Gibson is as follows:
Ai = F(LE, lE, PE) - + +
where Ai is the first difference of the interest
rates, and LE, lE, and PE are liquidity effects, income ef-
fects and price expectation effects respectively. The signs
below indicate the direction of the effects on interest
rates. The functional relation used by Gibson is as fol-
lows: ^ ^ { (ijií. A 9M r • ^ 9t H gt t' S. 3t ' t-l' ' M 9t t-n
Phillip Cagan (1972, 1969) examined the relationship
between changes in the rate of change of money (M2) and
changes in the commercial paper rate, using reference cycle
data. He found that an increase in the monetary growth rate
in stage t has a negative effect on interest rates in stage
t, zero net effect in stage t+1, and positive effects there-
after. The model used by Phillip Cagan is as follows:
Ai = a + Bj AM + ^2^^-! '^ 3 t-2 •*" "'' n+î' t-n
Friedman's (1961) study indicated that the total lag
derived from the specific money cycle turning point is 18
months for the peak and 12 months for the trough. A study
20
similar to Friedman's is that authored by Friedman and Anna
Schwartz (1963a) in which they employed two differential
techniques, using the turning-points approach to estimate
lag. The first approach was to compare turning points of
business cycles and the second technique was to compare the
"step dates" in the rate of growth of the money stock with
turning points of the business cycle. Friedman and Schwartz
estimated the mean lags of monetary policy to be two quar-
ters for both peak and trough.
In a U.K. money-demand study examining U.S. results of
Friedman and Schwartz and U.K. data, Walters (1965) found a
strong significant relationship between the level of nominal
income and the level and change in the quantity of nominal
money. The regression results estimated the relation for
the U.K. using annual observations of nominal income on nom-
inal money balances for the period 1877-1962 and measuring
variables in the log form. The model used by Walters is as
follows: oo ^ ^ > = iSo V i "(T-t)
Woll (1972), using the more realistic but statistically
more complex concept of distributed lags, carried out a
study of the Federal Republic of Germany during the period
1952-1967 on the relationship between a change in the
quantity of money and the change in the interest rate. Woll
21
presumed that a change in the quantity of money would depend
on a constant K, the change in the interest rate i and the
change in the quantity of money in the previous period:
AM = K + a (Ai) + 6 (AM)
Woll in this study found that the length of the lag for
an expansionary monetary policy was far shorter than the lag
length for a contractionary monetary policy, a clear confir-
mation of the argument that monetary policy is not symmetri-
cal.
Manfred J. M. Neuman (1977) in his own study on the
Federal Republic of Germany (1960-1974) investigated the de-
terminants of the nominal rate of interest for an open econ-
omy, given a fixed-exchange-rates regime. A credit market
model (an extension of the Brunner-Meltzer theory of the
monetary process to an open economy) of the monetary sector
was formulated, and a reduced form solution for the interest
rate was derived. Neuman concluded that the conventional
approximation of the anticipated rate of inflation by an es-
timated polynomial lag of actual rates of inflation is in-
ferior to the use of the difference between bond and divi-
dend yield. Estimates from this study showed that an
increase of the anticipated rate of inflation by one
percentage point raises the German nominal rate of interest
by about fifty basis points during the same quarter and
symmetrically depresses the real rate on financial assets.
22
Jack Carr, Lawrence B. Smith and James E. Pesando
(1976) investigated the relationship between price expecta-
tions, income taxes and the nominal rate of interest in Can-
ada. The approach utilized the rational expectations hy-
pothesis to create a synthetic price expectations series.
Using Canadian data, these series were applied to four mod-
els of the determination of the nominal interest rate: the
Yohe-Karnosky (1969) model, the Carr-Smith (1972) model, the
Feldstein-Eckstein (1970) model, and the Jenkins-Lim (1973)
model.
This study also examined the Darby hypothesis that in-
come tax consideration will cause nominal rate of interest
in equilibrium to increase by more than the increase in the
expected rate of inflation. In the context of the four mod-
els of interest rate determination, the hypothesis that the
price expectations coefficient is significantly greater than
one was tested. The standard procedure for generating price
expectations was used, and it is the procedure which assumes
that individuals employ only the information contained in
the past history of inflation when formulating their fore-
casts of future inflation. Based on this assumption the
weights on lagged prices are estimated. This study was
inconclusive with respect to the Darby hypothesis that tax
considerations will cause nominal rate of interest to
23
increase by more than the increase in the expected rate of
inflation.
Eugene F. Fama (1975), in an innovative and provocative
study concerned with efficiency in the market for one-to
six-month U.S. Treasury Bills, provided indication that at
least during the 1953-1971 period, there was a definite re-
lationship between the present nominal rate of interest, and
the rate of inflation subsequently observed. Moreover, dur-
ing this period, the bill market seemed to be efficient in
the sense that nominal interest rates summarized all the in-
formation about future inflation rates. There was also an
indication that the real rate of interest, ignoring taxes,
seemed to be constant during this period.
Fama's methodology was drawn on the fact that the dif-
ference between the market interest rate and the subsequent
observed rate of inflation, the ejí post real interest rate
consists, by definition, of the ex ante real interest rate
plus a pure forecasting error. The hypothesis of market ef-
ficiency implying that these forecast errors must be serial-
ly random. Thus, observing ex post real rates is equivalent
to observing ejí ante real rates with random error
measurement.
In a follow-up study, Nelson and Schwert (1977) using
the same series of data as Fama (1975) concluded that
expectations of inflation have accounted for most of the
24
variation in short-term interest rates during the postwar
period, and that those expectations embody significant in-
formation beyond that contained in past inflation rates
alone.
Thomas Sargent (1973), in an earlier study of the rela-
tionship between nominal rate of interest and the rate of
inflation anticipated by the public, used a simple linear
dynamic macroeconomic model. The model was Keynesian in
structure, but it assigned important roles to price level
adjustments and anticipations of inflation. In the long
run, the model was quite classical in behavior.
Sargent ignored technological change and growth in sup-
plies of factors of production. As a consequence, he as-
sumed the full-employment level of national income to be
constant over time, where full-employment level of national
income meant that level of income which is consistent with
price stability. He further assumed that the government
neither spends nor taxes, a simplification that he argued
never affected the character of the results.
The real side of the model consisted of standard post
Keynesian consumption and investment functions. Desired
real consumption at time t was assumed to be determined by
permanent income. Money and prices were integrated into the
model via a demand function for nominal balances and a
version of the Phillips Curve.
25
Sargent concluded from this study that the relationship
between anticipated inflation and the nominal rate of inter-
est is in principle more complex than depicted by Irving
Fisher's famous formula. In addition, the perceived real
rate of interest is not a constant and thus assuming con-
stancy of the perceived real rate of interest, as had been
done in most empirical applications of Fisher's equation, is
quite a restrictive specification.
Maurice D. Levi and John H. Makin (1978) extended the
approach first undertaken by Robert Mundell (1963), of em-
ploying a general equilibrium model to question the Fisher's
(1930) hypothesis that the real rate of interest is invari-
ant with respect to changes in anticipated inflation. The
extension involved the inclusion of a labor sector and the
incorporation of the effect of taxes on nominal interest
rates as discussed by Michael Darby (1975). Money wages
were assumed to be rigid downward.
The proposition advanced in this study was that the
Fisher equation ought to be viewed as a reduced-form rela-
tionship derivable from a simple general equilibrium model,
and this model should allow for the impact of a number of
factors which affect the nominal rate of interest. These
factors include taxes on interest earnings; induced changes
in income and employment which may accompany a change in
26
anticipated inflation; real balance effects; and the size of
the interest elasticity of the demand for money. Levi and
Makin accounted for these factors by introducing a macro-ec-
onomic model which determines the impact of changes in ex-
pected inflation upon the nominal interest rate. The closed
economy model consisted of equilibrium conditions in commod-
ity, money, and labor markets with the bond market eliminat-
ed by Walras' law. The money market was expressed in stock
equilibrium terms.
The results of this study suggested that the role
played by income effects, as opposed to that played by real
balance effects, in affecting the impact of anticipated in-
flation upon nominal interest may vary over time due to
changes in the elasticity of money wages demanded with re-
spect to prices. A shift in that parameter may help to ex-
plain the discovery by Lahiri, Gibson, and William Yohe and
Denis Karnosky, of a break occurring about 1960 in the meas-
ured impact of anticipated inflation on nominal rate of in-
terest.
Ignazio Visco (1975), with a model identical to Sar-
gent's, except for the inclusion of a real balance effect
upon expenditure, showed that even in Sargent's dynamic
model after full adjustment, Mundel's comparative static
real balance effect is preserved, whereby a change in
27
anticipated inflation permanently affects the real interest
rate.
Kajal Lahiri (1976), in a doctoral thesis, tested Fish-
er's two hypotheses independently, and then in a unified
framework. The two hypotheses are; (1) that the nominal in-
terest rate for a particular asset with returns fixed in
money terms is equal to the real rate of interest plus in-
flation and (2) that distributed lags on past prices can be
used as observable proxies for the supposedly unobservable
price change expectations. Four types of expectation hy-
potheses were used by Lahiri: the weighted or distributed
lag, the adaptive, the Extrapolative and the Frenkel expec-
tation hypothesis. Lahiri concluded that his calculations
supported earlier findings by Gibson and Turnovsky that both
the interest rate equation and the expectations formation
equation had a structural break around 1960. However, when
the adaptive expectation hypothesis was used, the Chow test
of equality of regressions coefficients did not support a
break in the reduced form interest rate equation.
In a quite recent empirical investigation, Scott Hein
(1982) examined the evidence to determine whether money
demand behavior over the last two years has been erratic
enough to justify the observed volatility in money growth.
28
Hein provided evidence on short-run (quarterly) money
growth volatility. The methodology was to plot, for each
quarter since 11/1962, quarterly money growth (at an annual
rate) less the average of money growth over the prior 12
quarters. The volatility had two different dimensions. One
dimension is simply the magnitude of the deviation from
trend, and the second dimension is the frequency with which
deviations of money growth, relative to trend, change signs.
The change of sign from positive to negative of the money
growth relative to trend was most frequent in the 1980-1982
period.
Hein, after empirically investigating the demand for
money (the relationship between real money balances on the
one hand and current interest rates, real income, and lagged
real balances on the other hand) using multiple regression
analysis, concluded that there is little from his simula-
tions to indicate a "shift" in the behavioral relationship.
Thus, he summarized,
both auxiliary arguments in favor of a behavioral shift in money demand in 11/1980 lack either log-ical foundation or supportive empirical evidence (p. 32).
In another recent study, Vance V. Roley (1982) used an
efficient market model to examine the relationship between
unanticipated changes in money and interest rates. This
model assumed that investors efficiently use all publicly
29
available information in setting interest rates in the money
market. Thus, the 3-month Treasury bill yield at 3:30 p.m.
on the day of the announcement should reflect the market's
expectation of the announced money change at 4:10 p.m.
The implications of the efficient markets model as ap-
plied were as follow: First, the movement of the 3-month
Treasury bill yield from 3:30 to 5:00 p.m. on the day of the
money announcement should depend only on information ob-
tained by investors between 3:30 and 5:00 p.m. Secondly,
any relevant information obtained between 3:30 and 5:00 p.m.
on the day of the money announcement should influence the
3-month yield during this period, but new information ob-
tained from the money announcement may significantly affect
the Treasury bill yield.
The results obtained showed that the market had become
much more responsive to unanticipated changes in money since
October 1979, a month in which the Federal Reserve announced
a change in its monetary control procedures. And Vance con-
cluded that the estimated results indicated that one source
of increased interest rate volatility is the greater respon-
siveness of the market to such unanticipated changes and
also that the greater responsiveness may represent rational
behavior by investors toward the new operating procedures.
30
In the same study, Vance undertook a further empirical
examination of the relationship between unanticipated chang-
es in money and interest rates. The objectives were to de-
termine the factors that influence the size of the response
and to identify the sources of the post-October 1979 rise in
interest rate volatility. The results from this examination
suggested that about 34 percent of the volatility of the
3-month Treasury bill yield since October 1979 may be di-
rectly attributed to an increase in the market's response to
unanticipated changes in the money supply.
R, W. Hafer and Scott E. Hein (1982) in another recent
study re-evaluated the evidence suggesting that the expected
(ex ante) real interest rate on short-term financial asset
is constant. Evidence was provided counter to the hypothe-
sis that the expected real rate of return on short-term fi-
nancial assets was constant over the period 1955-1979.
While rejecting the constancy hypothesis, this study also
provided evidence consistent with conventional macroeconomic
theory, whereby increases in real money balances temporarily
lower expected real rates. This effect was contemporaneous
on a quarterly basis. Also while such an effect was
significant, it was relatively small and was offset in the
following quarter by an identical rise in expected real
rates. Thus there was no evidence of a long-run effect
31
running from changes in real money balances to changes in
real interest rates. And finally, the evidence presented
suggested that a more volatile short-run real money growth
is likely to produce more volatile real interest rate fluc-
tuations.
In another recent empirical study, John H. Wood (1983)
examined whether the connections between interest rates and
inflation experienced since the early 1950's have, in fact,
differed significantly from those observed by Fisher, that
is, whether nominal interest rates lag rather than antici-
pate inflation according to the efficient markets model by
Eugene Fama. A secondary objective was to compare the abil-
ities of the Fisher's model, and the efficient markets mod-
el, to explain the data, both before 1930 and after 1950.
Wood's estimations provided evidence that the tendency
for changes in interest rates to lag changes in the rate of
inflation has been as pronounced recently as it was during
the 19th and early 20th centuries. In addition, the expla-
natory power of the Fisher's model was superior to the effi-
cient markets model for both 1915-1927 and 1953-1982 peri-
ods.
Douglas Fisher (1968), in a further empirical
investigation of the demand for money in Britain, used
quarterly data covering the period 1951 to 1967. The basic
data were the two definitions of money, namely Ml (currency
32
plus demand deposits) and M2 (Ml plus time deposits), the
various interest rates, and income arguments. The most im-
portant finding was that the possibility of a highly unsta-
ble demand for money function in Britain since 1951 was
found to be implausible. This possibility was emphasized in
the theoretical writings of the "new orthodoxy," and more
conjecturally, in the empirical work of A. A. Walters. The
demand for money in Britain was found to be a stable func-
tion and this demand for money function has a relative short
run interest elasticity. Thus results found for Britain
were close to those obtained for the United States.
In another study, David Laidler et al. (1970) did a
further investigation of the period covered by Douglas Fisn-
er (1968). The main conclusion from this study was that
Fisher seems to have overstated the stability of the simple
formulations of the demand for money function as far as
post-war Britain is concerned. The role of the rate of in-
terest in the demand for money function was left obscured,
since Fisher's model makes the demand for money depended
only upon permanent income.
M. J. Artis et al. (1976) carried out another follow up
study of the demand for money function in the United
Kingdom. They reached the conclusion that the demand for
money function was stable as far as post-war Britain was
33
concerned. Simultaneous equations rather than
ordinary-least-squares regressions were used in this study.
F. A. den Butter and M. M. G. Fase (1981), in another
study, examined the demand for money in EEC countries, pos-
tulating that desired nominal demand for broad money, M2,
depended on expected real income, the expected price level,
the expected long-term interest rate, the expected change in
the price level, and the expected level of economic activi-
ty.
The sample period for this study was from the 1960's to
1976. The period 1/1977 to IV/1978 was use for ex ante pre-
diction. The empirical estimates showed that in the nominal
demand for money functions, the long-run income elasticities
range from 0.77 (Denmark) to 2.33 (United Kingdom) and the
price elasticity was significantly greater than unity, with
the lowest value in Belgium (1.09) and the highest value in
the United Kingdom (10.89). The long-run interest rate
elasticities clustered around -0.20. However, the United
Kingdom's demand for money function, according to this spec-
ification, was stable in the 1970's.
Michael J. Hamburger (1977), in another study, examined
the properties of the demand functions for money in Germany
and the United Kingdom. The main purpose of this study was
to inquire how the openness and institutional setting of a
34
country may influence the demand function for money and the
definition of the quantity of money appropriate for that
function. One of the principal issues considered was the
question of what interest rate or rates provide the most ap-
propriate measures of the opportunity cost of holding money.
The model used by Hamburger postulated that desired (equi-
librium) money balances (M*) are a function of interest
rates (r) and a constraint (x) i.e.,
M* = M(r,x)
Regressions for quarterly observations of German and United
Kingdom data for the period 1963 through 1970 were used.
The equilibrium elasticity of the demand for money with
respect to the short-term interest rate was -0.07 in Germany
and the long-run nominal income elasticity for Germany was
between 0.900 and 1.00. This finding was in line with other
results that have been obtained for narrow definitions of
the money supply in the United States and the United King-
dom. The response of aggregate money balances to changes in
its determinants was found to be much faster in Germany than
in the United States. The entire response to interest rate
changes was found to occur after a lag of one quarter.
In many respects the results obtained for the United
Kingdom were similar to those for Germany. Interest rates
were important determinants of the aggregate money holdings
35
over the sample period. The preferred estimation equation
for the United Kingdom was about as stable as its German
counterpart.
The conclusion was that in Britain and Germany, as in
the United States, the quantity of money demanded appears to
be a relatively stable function of two arguments, income and
interest rates.
In a very recent study, W. W. Brown and G. J. Santoni
(1983) examined the relation between changes in money growth
and changes in interest rates for the United States. The
segmentation of the period of study was based on whether the
United States was on or off the gold standard. The periods
Brown and Santoni covered were 1914-1929, 1934-1953,
1954-1970 and 1971-1983. The conclusion from this study for
the period 1971-1983 was exactly as had been hypothesized on
the proposal of this research in 1982. The model was the n
same as that used in the present study. Ai = c + E A. H , k=0 t-k
However, there are some major differences in the stud-
ies; while the present study used the log form because the
basic data was money stock, Brown and Santoni used money
growth rate and thus no log form. Also while Brown and
Santoni apparently used the ordinary least squares
procedure, the Almon lag procedure was used in the present
study, and also while only the liquidity and inflation
expectations effects of a monetary disturbance were
36
addressed in their study, the present included discussions
on the income and loanable funds effect. The securities
used for the two studies also differ.
James G. Hoehn (1983) studied the response of interest
rates to fluctuations in money growth before and after Octo-
ber 1979 for the United States. The Federal Reserve adopted
a new method of monetary control in October 1979, when the
Federal funds rate was replaced by nonborrowed bank reserves
as the primary instrument for open market operations. His
major conclusions were: that alternative monetary procedures
affect the link between interest rates and money growth;
that the Federal funds rate showed stronger responses to de-
viations of money stock from target; that movements of the
Federal funds rate were linked more immediately to money
growth; and that the reserve based procedure facilitated
more aggressive responses of the the Federal funds rate to
money growth.
The model used is as follows:
n ALog (R ) = C + E A.ALog (Ml)^ . + U
L i=0 1 t-i t
where R is the Federal funds rate,
Ml is adjusted Ml,
C is a constant,
and U is the disturbance term.
37
Milton Friedman and Anna Schwartz (1982) studied the
monetary trend in the United States and United Kingdom. On
the empirical analysis regarding the relation of interest
rates to current and prior money change, they concluded that
although their theoretical framework provides an important
insight into the empirical behavior of interest rates, the
empirical results produced no simple generalizations that
would enable an observer to predict the effects on nominal
interest rates of a monetary change.
Among the authors' other major conclusions are:
1. A single demand function for money is applicable to the
whole century and to both the United States and the Unit-
ed Kingdom.
2. The interwar period is the only period that is consistent
with the Keynesian approach.
3. For the rest of the period, the data conform better to a
quantity theory approach.
4. Nominal interest rates were not appreciably affected by
expectations of inflation or deflation before the 1960's
but they have been dominated by such expectations since.
David Demery and Nigel W. Duck (1978) studied the
behavior of nominal interest rates in the United Kingdom,
from 1961-1973. Using both the Fisher hypothesis and an
extended model of Sargent's (1969) loanable funds model,
they arrived at these two major conclusions: First, that
38
nominal interest rates rise as expectations of inflation
rise, and secondly that nominal interest rates adjust infi-
nitely quickly from one equilibrium to another. Secondly,
that it takes about nine months for 75 percent of any dise-
quilibrium to be made up and more than 15 months for 90 per-
cent of any disequilibrium to be made up. Finally the main
policy conclusion was that, success in bringing down inter-
est rates is likely to be achieved only if permanent reduc-
tion in inflationary expectations is achieved. Any policy
that does succeed in reducing expected inflation will have
its full effect on interest rates only after two years.
As a follow-up to Demery and Duck's empirical analysis,
John Foster (1979) attempted to assess empirically the ex-
tent to which inflation has influenced short-term nominal
interest rates in the United Kingdom over the period
1961-1977. He thus extended Demery and Duck's period of
study by four years.
Conclusions drawn from this study were mixed. For
pre-1967 period, the conclusion was that there was strong
evidence that inflationary expectations are an important in-
fluence on short-term nominal interest rates. But for the
post-1967 period there is only limited evidence to support
the hypothesis that inflation expectations have any role in
explaining the nominal interest rates.
39
Summary of Literature
Nearly as rapid as the spread and adoption of the Fish-
er-Phillips curve, after its rediscovery in 1958, has been
the spread and adoption of the analytical separation of mon-
etary policy effects on interest rates into liquidity, in-
come and inflationary expectations. This approach has been
lucidly presented by Feldstein and Eckstein (1970), Gibson
and Kaufman (1968a,1968b), Friedman (1968a, 1961), Neuman
(1977), Friedman and Schwartz (1963a, 1982), Cagan(1965,
1972), Gibson (1970a, 1970b, 1972), Cagan and Gandolfi
(1969), and Sargent (1973). Darby (1975, 1976) incorporated
the financial effects. Unfortunately empirical implementa-
tions have suffered from both empirical and analytical de-
fects which have made interpretation of results less con-
vincing.
CHAPTER III
CONCEPTUAL FRAMEWORK
Survey Of Theoretical Underpinninqs
In this chapter a series of rudimentary economic models
will be covered, and an effort will be made to present them
in an ascending order of reality and advancement. First a
look will be taken at an economy in which there is no oppor-
tunity for exchange of goods or services. Every individual
is self-sufficient, depending only on the output of his la-
bor and other resources. Next a look will be taken at a
model in which there exists opportunities for exchange, but
all production and consumption takes place in the same time
period, thus there is no opportunity for saving and invest-
ment. The rate of interest therefore plays no role in such
an economy.
Next a model is covered in which the time preference
dimension and opportunity for investment and saving are in-
troduced and the rationale for lending and borrowing is ad-
dressed. Since the rate of interest determines equilibrium
in the credit market, equating the amount of borrowing to
the amount of lending, interest rate determination will then
be discussed, followed by two advanced theories of interest,
40
41
specifically the Loanable-Funds theory of interest rates and
the Liquidity Preference theory of interest rates. Also, a
review will be made of the equivalence of these two theories
and how this literature is related to this study.
Finally the various effects of a monetary growth dis-
turbance on the nominal interest rate will be covered, fol-
lowed by a presentation of the hypothetical model underlying
the study. The chapter will end with a summary of the role
of the rate of interest in an economy.
An Economy without any Exchange Opportunities
This is a hypothetical case, for there is no stage of
economic progress during which the phenomenon of exchange is
known to have been entirely absent. Free exchange will make
it possible for the society as a whole to achieve a higher
welfare than can be achieved under individual autarky. In
this model the individual utility or consumption preferences
are limited by his/her wealth and production function. Thus
without an exchange market, the maximization of wealth and
the maximization of utility cannot be separated.
42
Production and Consumption Takes Place in One Time Period
Let us now relax the assumption of no opportunities for
exchange, and now assume that though exchange of goods or
services is possible, all production and consumption takes
place in one time period. All of what is produced in time
period T is all consumed in that time period. In this model
the individual utility is no longer limited by his/her pro-
duction function because he/she can now exchange what he/she
produces but cannot consume for what he/she consumes but
cannot produce. In other words one's production decisions
can now be separated from one's consumption decisions. A
person who loves to produce potatoes but prefers to consume
oranges can trade with another person who loves to produce
oranges but prefer to eat potatoes. This exchange can take
place either by barter or via a medium for multisided ex-
change such as money.
However, within this society, economics entities cannot
save nor invest. Cultural advances in such a society are ei-
ther too slow or nonexistent since the accumulation of
wealth is necessary, although not sufficient, if a society
is to improve its lot and to make cultural advances
possible.
43
Time Preferences and Investment Opportunities
Continuing the process of refining the model, let us
add the time preference dimension and the opportunity for
investment and saving, to the opportunity for exchange. Now
the question is, why do economic entities save rather than
consume all what they produce as they did earlier when there
was no time dimension, and also why do they invest? Irving
Fisher's (1930) theory squarely addresses these questions.
Fisher argued that saving-investment behavior is influ-
enced by "investment opportunities" that increase the stan-
dard of living in the long run, the cost of undertaking such
opportunities being some sacrifice of consumption in the im-
mediate short run. Since people prefer more consumption to
less, they are induced to take advantage of investment op-
portunities that have high rates of return. In fact, all
investment opportunities whose rate of return are positive
potentially fulfill the preference for more consumption to
less.
Fisher again argued that besides investment opportuni-
ties, saving-investment behavior is also influenced by time
preferences that are biased toward an impatience to consume.
He argued that people generally prefer to consume a little
more now and a little less later than to pattern it the
other way around. Suppose you are asked: Would you rather
44
take one thousand dollars out of your next year's income to
have and spend now, or would you rather forego one thousand
dollars out of this year's income to have and spend next
year? Assuming no interest, if you are like most people,
you would prefer to spend the money this year rather than
next year. This is called the positive time value of money,
meaning a dollar today is worth more than a dollar tomorrow.
Impatience to consume works as a brake on investment.
The greater the preference for current consumption over fu-
ture consumption, the less it pays to invest. In conclusion
therefore, the actual investment decision is governed by
both the impatience to consume and opportunity to invest.
In a modern economy, a person can allocate current income
between consumption and investment in any proportions that
opportunities and the monetary unit of account permit. The
acts of investment and saving, in financially more developed
nations, can usually be separated. Investment is not tied
to saving because a person can finance investment alterna-
tively through borrowing. Similarly, saving is not governed
solely by investment because saving can be employed alterna-
tively by lending.
With financial markets, economic entities use their
investment opportunities, their subjective time preferences,
and the given market rate of interest, to determine
simultaneously their quantities of saving, investment,
45
lending, and borrowing. The emphasis on this central idea
of Fisher's theory is on the rate of interest. The next
task therefore is to explore the microeconomics determinants
of lending and borrowing.
Lending, Borrowing, and Time Preferences
Basically an individual will lend or borrow if his de-
sired pattern of consumption spending over time does not
match that of his income.
Using a basic economic model which in graphical exposi-
tion, the horizontal axis measures the quantity of some
scarce commodity available now, (period 0) CO, and the ver-
tical axis measures the quantity available one period from
now, (period 1) Cl. A representative individual is assumed
to be endowed with a set of resources such that he can have
COa if he works full time to produce only current goods.
Alternatively he could work full time to produce future
goods only. His maximum now will be Cla. For a graphical
illustration of this model, see Figure 1.
The concave line connecting COa and Cla represents the
maximum quantities of CO and Cl which this individual can
get on his own given his initial endowment and ability.
This is in effect the production possibility frontier or
46
Figure 1: Determination of the Interest Rate
47
transformation curve for the representative individual and
is normally assumed to be quasi concave or strictly concave
because of the law of increasing costs (The opportunity cost
of transforming Cl into CO or vice versa increases as more
and more Cl are transformed into CO and vice versa). The
slope of this curve, the marginal rate of transformation
measures the rate at which the individual can transform CO
into Cl.
Using PO as the price of CO with a numeraire value of
1. Because Cl is the same good only one period removed, its
price, Pl, in terms of the numeraire is 1/1+r, where r is
the current rate of interest. For now we assume r is given,
but later we will examine the determinants of r. The ratio
of the current price to the future price (PCO/PCl) is equal
to 1 / (1/1+r) or simply 1+r. This is the rate at which our
individual can exchange on the market CO for Cl or vice ver-
sa. Line AB has a slope equal to this price ratio, -(1+r).
In order to maximize the value of the resources which he
owns, this individual will produce at point E, (producing
COm and Clm units of CO and Cl, respectively) where the mar-
ginal rate of transformation over time is equal to the ratio
of future to present prices, that is where the exchange line
is tangential to the production possibility frontier. The
value of this individual's wealth, POCOm + PlClm is at a
maximum.
48
In this simple model, we have given the individual the
choice of income streams. He has selected to use his re-
sources in such a way that they generate COm units now and
Clm units in the next period. However, just because he has
chosen to produce at E, with the associated time stream of
income, does not mean that this is where he will choose to
consume. The maximization of his wealth and the maximiza-
tion of his utility or consumption preferences are two dif-
ferent things when there exists a market for exchanging
present for future goods. This is what Van Horne termed the
separation theorem (1978, p. 49).
Supposing that this individual has a time preference
function characterized by the indifference curve II. In or-
der to maximize his utility, given the constraint of market
prices, he will choose point F. In other words, he will
trade some of his future income for some additional present
income. In equilibrium, he will consume COf units of CO and
Clf units of Cl. But since he is consuming more present
units than he is producing himself, he must borrow the dif-
ference (COf-COm). At the assumed given market rate of in-
terest, he must pay back one year from now some of his
future income (Clm-Clf). This individual is a net borrower.
On the other hand, if the individual's preference function
is such that it is characterizes by the indifference curve
12, he will choose to consume at G. At this point he is
49
consuming less present or current income than he is
producing himself and more future income than he is produc-
ing. This he can do by extending credit or loaning some of
his current goods to those who want more than they now have.
In exchange they must pay him back at the market rate of in-
terest with future goods. Thus at the going market rate of
interest, he prefers to consume less now than he is current-
ly earning,
Only if the consumer's indifference curve is tangent to
the market price line at point E, in other words 13, will
his income stream coincide with his consumption preference
and in that case he will neither lend nor borrow. Further-
more, as the market rate of interest changes, in other words
as the slope of the line AB changes, some people who were
lending might become borrowers and vice versa. At any time,
however, those with indifference curves lying below point E
are ultimate lenders and those above point E are borrowers.
We should now be in a position to turn to the micro-vari-
ables which together determine the rate of interest.
50
Interest Rate Determination Using Credit Market Theory and the Edge-
worth Exchange Box
Since as previously implied in our model, interest
rates are prices for earlier availability, they like other
prices are determined by the interaction of supply and de-
mand. To illustrate the way these forces affect the rate of
interest and, in turn the rate of borrowing and lending, let
us extend our model to include two individuals, A and B,
each of whom has been endowed with some amount of CO and Cl.
Using an Edgeworth exchange box, with the axis having the
same interpretation as before and for convenience letting
individual A, represented in the left hand corner be endowed
with all of the Cl and no CO. Individual B, represented in
the upper right hand corner, endowed with all CO and no Cl.
By construction, their endowment points coincide at point E.
See Figure 2 for the illustration.
Through this point we can draw their indifference
curves lAl for A and IBl for B. Because of the different
values they place on marginal units of CO and Cl, there ex-
ist potential gains from exchange. Under the assumption
that these two individuals are so insignificant relative to
the market that they perceive themselves as price takers,
we can derive their offer curves, OA and OB. These two
curves show for each rate of interest, the maximum quanti-
51
CIA CIB
Figure 2: Interest Rate Determination in the Credit Market
52
ties that each individual would be willing to exchange on
the market. Where these two curves intersect, at point H,
is the only place where the market will clear. The price
line, which passes from point E through point H, has a slope
of -d + r) where r is the market rate of interest which
equates the amount A wishes to borrow with the amount B
wishes to lend. At this r, A ends up borrowing COa units of
CO from B, leaving B with COb. In exchange A must give up
his claim to Clb units of Cl to B, leaving himself with Cla.
We notice that A borrows exactly the same amount as B is
willing to lend and his payment of future income will equal
precisely the amount B will receive, that is the quantity of
credit supplied is exactly equal to the quantity demanded.
It is this interaction which determines the rate of interest
in the market. Both traders have moved to higher indiffer-
ence curves, IA2 and IB2. Of course, this equilibrium sat-
isfies the condition of Pareto optimality such that there is
no other rate of borrowing or lending which moves both par-
ties to higher level of preference.
It is important to note that in this our simple model
of individual units, there is absolutely no place for credit
or financial intermediaries, since they cannot survive in
53
our simplified environment in which the rate the borrower
pays is the same as the rate the lender receives. With the
inclusion of financial intermediaries, we will direct our
attention to more advanced theories of the determination of
interest rates. The division is between the neoclassical
loanable funds theory and Keynes liquidity preference theory
of interest.
Loanable Funds Theory of Interest
Rate
The notion that the interest rate is determined by the
flow of funds supplied and demanded is the basis for the
neoclassical loanable-funds theory. In order words, the
loanable-funds theory of interest implies that interest rate
will be at equilibrium when it is at a level which equates
the demand for and supply of loanable-funds. Fisher's pure
form of the nonmonetary loanable-funds theory was stated in
terms of desired lending and desired borrowing. It was this
nonmonetary structure of the theory, it will be remembered,
that Keynes attacked as the classical theory of interest.
Figure 3 is an illustration of the loanable-funds theory.
54
0 % ' % Q Q
Figure 3: Equilibrium in the Credit Market
55
Sources of Supply and Demand of Loanable-Funds
The major sources of supply of loanable-funds are:
(1) Savings by households.
(2) Budget surplus by local, state, or federal govern-
ment.
(3) Increase in the money supply by the central bank.
(4) Dishoarding.
(5) Increase in financial liabilities by business firms
and financial institutions.
(6) Capital inflow from abroad.
On the other hand the main sources of demand for
loanable-funds are as follows:
(1) Investment by households and business firms.
(2) Hoarding.
(3) Budget deficit by local, state, or federal govern-
ment.
(4) Decrease in money supply by financial institutions
and government.
(5) Decrease in financial liabilities by business firms
and financial institutions.
(6) Capital outflow to foreign countries.
To state the loanable-funds theory in equation form, let us
designate Qs as the aggregate sum of all the supply
56
component sources and Qd as the aggregate sum of all the
demand component sources. Then the equation is
Qd = Qs (1)
The assumption that the aggregate supply and demand curve
will cross at some positive rate of interest appears to be
generally accepted by economists of all schools, though the
Keynesians in particular do not assume that Qs and Qd would
necessarily intersect at positive rates of interest under
conditions of full employment.
This contention is based on Keynesian theory rejection
of Say's Law, by questioning the ability of the interest
rate to synchronize the saving and investment plans of hou-
seholds, businesses and government. More generally this
view holds that savers and investors are essentially dis-
tinct groups that formulate their saving and investment
plans for different reasons which, in each instance, are
largely unrelated to the rate of interest. The fact that
modern capitalism is amply endowed with an elaborate money
market and a wide variety of financial institution does not
diminish this skepticism about the interest rate as a mecha-
nism capable of connecting the saving drain and the
investment spigot.
57
Liquidity-Preference Theory of Interest Rate
In his General Theory of Interest, Employment and Mon-
ey, John Maynard Keynes (1936) lauded a vigorous attack on
what he called the "classical" theory of interest, and pre-
sented what appeared to be an entirely new theory. It dif-
fers from the loanable-funds theory in three important
aspects:
(1) It focuses on the supply and demand for money as
the principal determinants of the interest rate.
(2) It analyzes the interest rate in terms of the stock
of money supplied and demanded, whereas the loana-
ble-funds theory analyzes the flow of changes in
the money stock.
(3) It focuses on the determination of the "nominal"
rate whereas the loanable-funds theory is primarily
concerned with "real" rate and quantities.
However, Keynes was also later accused of omitting the
real balance effect in his theory. The basic elements of
the liquidity preference theory are that the rate of inter-
est is determined in the first instance by interaction of
the supply of and demand for money stock and the demand for
money varies inversely with the interest rate because of
asset holders preferences for liquidity.
58
The logic for the inverse relationship according to the
modern opportunity cost theory is that since money is the
most liquid asset, people prefer to hold it over other as-
sets if the sacrifice of returns, which could be earned by
other assets is sufficiently small. Such is the case at ex-
tremely low interest rates. At higher interest rates, how-
ever, the sacrifice becomes larger, inducing asset holders
to switch out of cash balances and into earning assets.
Thus, people will hold less money at high rates and more at
low rates, giving a downward sloping demand-for-money curve.
Thus in mathematical equation form
9M . 9M , v __d / . s _ (2) 81 ^ ° ' ã " - °°
where Md is the demand for money,
Ms is the supply of money,
i is the nominal interest rate,
9Md, and |i are the first differentials.
The supply of money is assumed to be exogenously determined
by a central monetary policy making body, the central bank.
For a graphical illustration of the liquidity preference
theory, see Figure 4.
Keynes original explanation of the downward sloping de-
mand-for-money curve, in contrast to the modern opportunity
cost theory, was based on expectations and uncertainty as to
the future course of the rate of interest. He argued that a
given supply of money stock will not have a definite quanti-
59
Figure 4: Equilibrium in the Money Market
60
tative relation to a given rate of interest. What matters
is not the absolute level of the rate of interest, but the
degree of its divergence from what is considered a fairly
safe level.
Given any state of expectation, he reasoned that there
are two reasons for expecting that a fall in the interest
rate will be associated with an increase in the demand for
money.
(a) First is the argument that, if the general view as
to what is a safe level of interest is unchanged,
every fall in the interest rate reduces the market
rate relative to the "safe" rate and therefore in-
creases the risk of illiquidity.
(b) Secondly every fall in the interest rate reduces
the current earnings from illiquidity, which are
available as a sort of insurance premium to offset
the risk of loss on capital account; by an amount
equal to the difference between the squares of the
old rate of interest and the new.
Both the increase in the risk of illiquidity and the reduc-
tion in the current earnings from illiquidity will tend to
increase the preference for liquidity (money).
61
Keynes analyzed three broad motives of why there is a
desire to hold cash (1936, pp. 195-196):
(1) The Transaction-motive—that is the need of cash for
current transaction of personal and business exchanges. He
further subdivided this transaction-motive into:
(a) The Income-motive—The reason for holding cash here
being to bridge the interval between the receipt of
income and its disbursement.
(b) The Business-motive—Similarly cash is held to
bridge the interval between the time of incurring
business costs and that of the receipt of sale pro-
ceeds; cash held by dealers to bridge the interval
between purchase and profit realization being in-
cluded under this heading.
(2) The Precautionary-motive--Money is demanded here to
provide for contingencies requiring sudden expenditure, and
unforeseen opportunities of advantageous purchases, and also
to hold an asset of which the value is fixed in terms of
money to meet a subsequent liability fixed in terms of mon-
ey.
(3) The Speculative-motive—The object of holding cash
here is securing profit from knowing better than the market
what the future will bring forth.
62
In equilibrium the demand for money equals the supply
of money. The interest rate of money at a point in time is
then the primary equilibrating force. This theory is also a
partial equilibrium theory.
The Equivalence of the Liquidity Preference and Loanable-Funds
Theories of Interest
The discussion here is focused on the problem of wheth-
er the loanable-funds flow theory can be expressed as a
stock theory of the bond market. As noted earlier, the li-
quidity preference theory is formulated in terms of the de-
mand for money as a desired stock of money and the supply of
money being the existing stock of money. The loanable-funds
theory, on the other hand, is concerned with the demand for
and supply of a flow of loanable funds or bonds over a peri-
od of time; it is a flow theory, so even that part of it
which is concerned with desired and actual supply of money
is concerned with flows--the change in the desired and actu-
al stock of money over a period.
If a flow theory can be converted into a stock theory
(or vice versa) without any change in its implication, then
the difference between the loanable funds theory and the
liquidity preference theory is seen to be unimportant.
63
Patinkin (1959) argued that a flow theory is equivalent
to a stock theory if the assumption is made that individual
makes decisions with respect to flows over time T, as in the
loanable-funds model, and this can be shown to be equivalent
to a liquidity preference model where the individual is, in-
stead, concerned with the stock at the end of the period,
instant T+1. Patinkin concluded that the fact that the li-
quidity preference model is framed in terms of stocks and
the loanable-funds model in terms of flow is an insignifi-
cant distinction if we assume that the stock model refers to
end-of-period stocks. Also if the stock model refers to be-
ginning-of-period stocks in discrete time, the liquidity
preference and loanable-funds models are equivalent if we
assume perfect foresight.
A second problem is that even if a theory in terms of
flow concepts can be expressed equivalently in terms of
stock concepts, the liquidity preference and loanable-funds
theories would still differ because the former considers the
rate of interest to be determined by the demand for and sup-
ply of money whereas the latter considers the rate of inter-
est to be determined by the demand for and supply of bonds.
However, Hicks (1967) demonstrated that this distinction is
insignificant in a general equilibrium model where Walras's
Law holds.
64
Of the two theories of interest, the liquidity
preference theory is probably better suited for handling the
analysis of this study, the reason being that the equilibri-
um concerned with in the research is that in the money mar-
ket.
The Various Effects of a Monetary Growth Disturbance on the Nominal
Interest Rate
The Liquidity Effect
The theoretical basis for the liquidity effect is
grounded in the liquidity preference theory of interest.
And the argument here is that an expansion of the money sup-
ply will initially lower the nominal interest rate because
there will be excess money supply in the money market at the
existing nominal interest rate. This decline in the nominal
interest rate is the liquidity effect and this decline oc-
curs because a drop in the interest rate is necessary to
bring the demand for liquidity in balance with the supply.
The Income Effect
An expansion of the money supply will, as mentioned
above, lead to an excess money supply at the existing nomi-
nal rate of interest. Economic agents in their efforts to
eliminate the excess money supply in the money market or the
desires to bring the demand for liquidity in balance with
65
the supply, will purchase additional assets with their ex-
cess cash balances. Also the lower nominal interest rate
will stimulate capital expenditures on the part of business
and others. The mechanism leading to the stimulation of
capital expenditures is the income effect.
The Fisher or Inflationary Expectations Effect
Over time the increase in the demand for assets in an
effort to reduce the excess cash balances will cause both
income and prices to rise. When prices rise, lenders, in an
effort to protect themselves against the depreciation of the
real money value due to inflation, will add an additional
premium to the real interest rate. This upward adjustment
of the real rate due to expectations about a rise in the
price level is the Fisher effect.
The Financial Effect
This effect comes about as a result of the temporary
change in the banking system demand for short-term negotia-
ble bonds following an increase or decrease in the growth
rate of the money stock until loans to private customers are
expanded or contracted in proportion to the multiple
expansion or contraction of bank deposits.
66
Exposure of Hypothetical Model
The theoretical framework of our model is based on the
dynamic of the four effects of a monetary growth disturbance
on the nominal interest rate, specifically the liquidity,
the loanable-funds or financial, the income, and the infla-
tionary expectations or the Fisher effect. As discussed
previously, these effects do not all work in the same direc-
tion. The liquidity effect is a negative effect, while the
income and the inflationary expectations are positive ef-
fects. The initial phase financial effect is negative while
the second phase financial effect is positive.
It therefore means that a change in the growth rate of
the money stock which affects liquidity, inflationary expec-
tations, financial institutions' portfolios and income will
cause a movement in nominal interest rate in a direction
that cannot be determined a priori. If the combined liquid-
ity and the initial phase financial effect or what Milton
Friedman and Anna Schwartz (1982, p. 483) called the "first
round loanable-funds" effect dominates, then we would expect
a movement of the nominal interest rates in the opposite di-
rection to that of the change in the growth rate of the
money stock.
^ For an analysis of a combined liquidity and the first round loanable-funds effect, see Milton Friedman and Anna J. Schwartz (1982).
67
However, if the arithmetic sum of the inflationary
expectations, the income and the second-round-loanable-funds
effect dominates, then we would expect a movement of the
market interest rates in the same direction as the change in
the money stock growth rate.
In our hypothetical model, let us consider an economy
which starts initially at an equilibrium point A (see Figure
5 for the illustration), where money stock is Msl and market
interest rates is rl. Let the money stock in the economy be
increased from Msl to Ms2. Because of the liquidity effect,
and initially the financial effect, the rate falls from rl
to r2 where the demand for and supply of money are again in
equilibrium at point B. Income would respond to an increase
in the money stock via the real balance effect and eventual-
ly the income, and later the financial effect will shift the
demand curve from Mdl to Md2 where another temporary equi-
librium is reached at point C ^ In this special case, the
liquidity, income and financial effect completely offset
each another and the nominal interest rate returns to its
initial level. Of course in a real world setting, these ef-
fects may not completely offset each other.
2 This shift takes place only after some readjustments in portfolios by banks, households and businesses.
68
Figure 5: Hypothetical Model
69
If now expectations develop in the economy that the
rate of price change will rise, then the price expectation
effect will cause the demand curve to move upward further,
from Md2 to Md3 where equilibrium is reached at D.^ Thus
for a case in which the liquidity, income and financial ef-
fect offset each another and an inflationary expectation de-
velops, the market interest rate will rise to a higher level
than the level before an increase in the growth rate of the
money stock.
A key assumption in this model and thus in the subse-
quent reduced equation analysis, is that the demand for mon-
ey function is stable. This assumption is not unrealistic
considering the assertion of Friedman and Schwartz (1982)
that a single demand for money function is applicable to the
"3 .
' The rationale behind the price expectations shifting the demand for nominal balances is that in a period of rising prices, ceteris paribus, a proportionately larger money bal-ance is needed to carry out the larger anticipated nominal expenditures. Also rational investors taking into consider-ation the fact that interest payments to be delivered in the future as well as the principal payment will have less real value due to rising prices will charge a premium. On the other hand, borrowers considering the fact that interest payment expenditures will be tax deductible expenses will willingly accept the interest premium and this will again imply an upward bias on the market interest rate.
Also borrowers anticipating inflation will increase their demand for loans, since any principal obtained now is to be repaid in the future with dollars that are less in real value. As a consequence this effect will reinforce the shift of the demand for money curve upwards.
70
whole century to the United States and United Kingdom.
Therefore any change in the relation between the quantity of
money and the interest rate is due to an exogenous change in
the nominal money supply and not to any structural change in
the demand for money function. The implication in this case
being that any change in the liquidity preference function
is a movement along the demand curve and not a shift in the
demand curve.
Role of the Rate of Interest in an
Economy
Each person or corporation or government unit may feel
free to make saving and investment decisions, but they are
not really as free as they think. The different individual
decisions of participants in the market must be balanced.
If everyone decided to invest more than they saved, then
everyone would need to borrow, but none could, because there
would be no lenders.
Fortunately, the balancing process is facilitated
through the movement of interest rates toward an equilibri-
um. The interest rate (price of lending and borrowing
transactions) adjusts rapidly so that those who want to
borrow can find willing lenders and those who want to lend
can find willing borrowers. If everyone wanted to borrow,
the rate of interest would quickly rise to such a high level
71
that enough participants would change their minds and decide
to lend instead. The fact that the rate of interest adjusts
freely and impersonally in the market means that market par-
ticipants can behave as if their decisions are independent
of each other. The rate of interest is the "invisible hand"
that coordinates financial behavior in financial markets.
The role of the rate of interest in the financial market is
no different from any other price in any other market.
We have developed in this chapter several models, all
leading to the major goal of illustrating the role of the
interest rate in an economy and the determination of this
rate of interest. We have also covered the hypothetical
model, the two major theories of interest rate and the ques-
tion of their being equivalent, the various effects of a
monetary disturbance on the interest rate. The models de-
veloped in this chapter will be assumed in subsequent chap-
ters.
CHAPTER IV
METHOD AND PROCEDURES
The goal of this chapter is to provide an exposition of
the methodology and the procedures used as main vehicles for
carrying out the research. First, the basic data used for
the study are specified and the definitions of the various
monetary aggregates for the three countries as specified by
the central monetary authorities of each country are exam-
ined.
Next there is a brief coverage of polynomial distribut-
ed lags (both finite and infinite distributed lags), fol-
lowed by an examination of the Almon polynomial distributed
lag, which as stated earlier, is the main analytical tooi.
Some inherent advantages of the Almon lag over the ordinary
least square method and the Pascal's distributed lags are
discussed. Also examined are the characteristics of the ar-
rangements for monetary control in each of the countries.
And finally the chapter ends with a discussion of the Chow's
test and the dummy variable test, both of which are proce-
dures used to test for any structural divergence within any
time period in consideration.
72
73
Basic Data and Definitions
The basic data are monthly and quarterly time series
for both the money stock and the interest rate. The money
stock are in levels, both seasonally adjusted and seasonally
unadjusted. For the simple reasons that the components of
the monetary aggregates for the three countries are not uni-
form and the start dates of availability of the source data
are different, we will analyze the different definitions on
a country by country basis starting with the United States,
followed by the United Kingdom, then the Federal Republic of
Germany.
United States Data
Money
For the United States, the monthly time series data are
monthly averages of daily figures. These data are available
for the entire anticipated period of study, 1959-1983 and
were revised March 1982 by the Federal reserve Board of Gov-
ernors. The quarterly time series were estimated from
monthly averages.
1 For a complete list of the monthly series, see Appendix B and for a list of the sources of data, see Appendix A.
74
Interest Rates
The interest rate series we used was that on the 91-day
Treasury bill.^ We felt that the 91-day security will be su-
perior to intermediate and long-term security for the fol-
lowing basic reasons:
(1) Short-term securities are more sensitive to market con-
ditions than intermediate and long-term securities and are
therefore more likely to give a better picture of market
forces.
(2) The market in short-term Treasury securities possesses
great "depth and breadth." This security is demanded as a
liquidity vehicle in large amounts by all categories of
large money market investors; commercial banks, nonbank
financial intermediaries, state and local governments,
foreign governments and foreign banks, industrial corpora-
tions and nonprofit institutions.
(3) The default risk on Treasury bill is virtually nonexis-
tent as well as the callability feature and the differen-
tial tax treatment.
(4) They can be converted into cash at any time by selling
them in the most active of all secondary financial
markets.
^Also see Appendix B for a complete list of the monthly se-ries. Again the quarterly series were estimated from the monthly averages.
75
United Kingdom Data
Money
Our monthly time series data for the United Kingdom re-
late to "banking months" and not calendar months, because
calendar month data are not available. Each "banking month"
ends on the third Wednesday of the named month, except for
banking December which ends on the second Wednesday of De-
cember. Thus banking months vary in length. Also monthly
series before 1971 of the various monetary aggregates for
the United Kingdom are not available as only quarterly time
series were reported by the Bank of England until 1971. And
the series have different start dates related to the avail-
ability of the source data. The start dates are: October
1971 for Ml; July 1971 for M3, and May 1975 for PSL2. No
comparable United Kingdom series exist for L. For a list of
the U.K monthly time series, see Appendix C.
Interest Rate
For the United Kingdom, we use the three-month Treasury
bill rate.-'
^ For reasons why we use this interest rate, see an earlier discussion on this topic in Chapter IV.
76
Federal Republic of Germany Data
Money
In line with International practice, the Bundesbank has
defined various concepts of the money stock in the broader
and the narrow sense. A special feature in the Federal Re-
public of Germany is the concept of the central bank money
stock.
Our monthly series of Ml, M2, and M3 for Germany are
calculated from banking statistics, and are based on end-of-
month figures. Seasonally adjusted figures for Ml, M2, and
M3 as well as non-seasonally adjusted figures for M3 are not
available before 1969 because records of these monetary ag-
gregates were never kept.
Interest Rate
Also in line with international practice, Germany has a
Treasury bill rate; though with a slightly different maturi-
ty, 2 to 3 months. We use this interest rate and for rea-
sons why it was chosen, see an earlier discussion on the
topic in chapter IV.
^ For a complete list of the monthly series for the Federal Republic of Germany, see Appendix D. Also there is no com-parable series for the monetary aggregate L, as in the Unit-ed States. See also the Deutsche Bundesbank Special Series No. 7 for a comprehensive coverage on the money stock defi-nitions.
77
An Overview of Institutional Arrangements for Monetary Control within the Three Countries of the
Study
In an OECD Monetary Studies Series, institutional ar-
rangements in ten OECD countries (including the United
States, the United Kingdom, and Germany), may broadly be di-
vided into two groups; Type 1 and Type 2 systems.^
In Type 1 systems, authorities mainly operate on the
portfolio behavior of the commercial banks to influence
their liabilities directly. The most straightforward exam-
ple is the monetary-base control, a version currently prac-
tised by the Federal Reserve System of the United States.
Banks are require to maintain a minimum ratio of cash re-
serves to deposit liabilities, so that the size of the for-
mer imposes a ceiling on the level of the latter. The cen-
tral bank manipulates the size of bank's cash reserves (its
own liabilities) through open-market operations, and its own
lending policies with respect to the commercial banks (dis-
counting mechanism). Interest rates adjust to equate demand
and supply in the money and credit markets, and there is no
resort to administrative control on bank credit. An essen-
tial feature of such a system is that the central bank is
independent of the budget financing process. That is to
5 See Adrian Blundell-Wignall and Jean-Claude Chousaqui (1981).
78
say, the monetization of the public debt by financing
through the central bank is in no sense automatic.
Type 2 systems, on the other hand, are characterized by
attempts to control the money supply through its asset
counterparts by operating essentially, via administered in-
terest rates, on the portfolio behavior of the private non-
bank sector. Typically interest rates are set to influence
private sector's direct demand for government bonds which,
given the budget deficit, indirectly determine the govern-
ment's demand for bank credit. At given interest rates, the
banking system is normally committed to provide finance for
the budget deficit, and changes in the desired level of cash
reserves are readily forthcoming from the central bank. Of
the three countries in this study, the United States typi-
cally belongs to the Type 1 system, while the United Kingdom
typically belongs to the Type 2 system.° The German authori-
ties attempt to target all money aggregate affected by
switching between different type of bank deposits by non-
banks in response to interest rate changes, and some atten-
tion is paid to the interest elasticity of the demand for
money. However, it is on the liquidity and behavior of the
^ At least until 1981. Reforms in recent times in the Unit-ed Kingdom monetary policy include the abolition of the "corset," the imposition of a uniform cash reserve require-ment and more emphasis on the interest rate flexibility in general.
79
commercial banks that the German authorities operate
directly to achieve targets for some definition of the li-
abilities of the latter. In a broad sense, Germany can
therefore be considered as belonging to the same system as
the United States, the Type 1 system.'
Specification of Methods and Procedures
The basic analytical tool utilized in this study was a
polynomial distributed lags model, specifically the Almon-
lagrangean interpolation polynomial lag. The polynomial
distributed lag estimation technique forces the coefficients
of each lagged variables of an equation to lie on a polyno-
mial of degree P. In the presence of a high degree of mul-
ticollinearity, ordinary least squares estimates are not
precise. Thus, the rationale for the use of the polynomial
^ Also an obligatory minimum reserves system was introduced in Germany after the second world war but unlike in the United States it was intended to give the central bank a flexible and effective instrument of liquidity policy. Also the Bundesbank first engaged in open-market operations in the money market in 1955 and again unlike the United States, open-market operations in long-term securities are permitted only for the purpose of regulating bank liquidity and never for the primary aim of financing the public borrowing re-quirement or supporting the market as the Federal Reserve did before the Federal Reserve-Treasury accord in 1951, whereby the Federal Reserve was no longer under any obliga-tion to support government bonds. And finally the Bundes-bank regards only the central bank money stock as its inter-mediate target variable and central money indicator rather than Ml, nor M2, nor M3.
80
distributed lag technique is that it increases the precision
of the estimates. Estimates of the individual lag weights,
however will be biased generally unless the correct lag
length and degree of polynomial are specified. Therefore it
is important that the appropriate specification be deter-
mined, and there are a number of procedures and criteria for
determining the appropriate lag length and polynomial de-
gree."
The regressor variable for the study was the distribut-
ed lag first difference of the log of the money stock, while
the dependent variable was the first difference of the log
of the short-term Treasury bill rate. In a more general
form this is the model used:
ALog (RT ) = C + jl^ IQ W. ALog (M. _ ) + U ^ 3 j
where RT = Short-term Treasury bill rate,
W = Unknown constant or weight,
^ There is the minimum standard error (minimum variance) criterion used by Schmidt and Waud to investigate the lag lengths for the individual variable of the St. Louis equa-tion. Sometimes the minimum standard error is used in con-junction with the maximum R^ criterion. This was also used by Peter Schmidt and N. Waud. For a complete analysis of these criteria, see Peter R. Schmidt (1974); Peter R. Schmidt and Roger N. Waud (1973); Theil Henri (1971).
In addition, there is the Pagano-Hartley technique, a very computationally efficient procedure. For a complete discussion of the P-H technique, see Marcello Pagano and Mi chael J. Hartley (1981).
81
M = Money stock variable, uncorrelated with the
disturbance term,
U = the disturbance or error term, with a mean value
of zero and constant variance,
and t = the time subscript (monthly or quarterly).
The Wij are called the lag coefficient structure
for every j = 1,2,3, K.
Formulation of equation (3) raises certain problems.
An infinite number of parameters are to be estimated, hence
the model is nonoperational. And if we truncate each lag
distribution at some point in time, for example N, we need a
priori information to select N. Economic theory generally
is not clear as to the exact shape of the lag distribution
nor is it exact in the number of lagged terms to be includ-
ed. It follows that in testing a distributed lag model one
must decide
A. On the lagged terms of each lag distribution to in-
clude, when a finite lag distribution is used.
B. On the shape of each lag distribution.
C. On the technique to employ in estimating the parame-
ters of the lag distribution.
If we introduce the assumption that the shape of the
lag structure in equation (3) follows a Pascal distribution,
that is H.. = (1-X) "" C " ^ " X , 0<X<1. i = 1.2,...k, i=i,.. 1 - •*- »
82
then our lag distribution becomes a Pascal distribution,
which is an infinite distribution in the sense that it rang-
es from zero to infinity.
However, if we introduce the following assumptions to
equation (3)
(1) ^^"^ ^t = ±h V i t ' ' =^'2,3,
(2) W^ are calculated at X = 0, ,N-1 for a
polynomial W(x) of degree M, where N is the number of
periods over which the distributed lag extended,
(3) If M + 2 points on the curve are known, b / all the W's
can be calculated as a linear combinations of those val-TTH-Í
ues by ^ = z $ b , then our lag distribu-^ r=0 ri r ^
tion becomes an Almon-lagrangean interpolation polynomi-
al lag.
We feel the Almon lag distribution will be superior to
any other procedure for the following reasons:
1. We have a priori knowledge that even under the as-
sumption of rational expectations, a change in the
growth rate of the money stock affects the market
interest rate with a lag. Thus we can avoid Peter
Schmidt and Roger N. Waud's (1973) criticism
against the Almon distribution lag.
83
2. The Almon distribution lag is superior to the Pascal
distribution lag if the calculated weights are as-
sumed to reverse signs, because by the nature of
the Pascal distribution the weights calculated do
not reverse signs.
3. The Almon lag is not only more flexible and superior
than any ordinary least square method, but previous
studies done using ordinary least square method had
encountered a severe problem of multicollinearity
and the weights had been known to fluctuate wide-
iy.9
When Almon first introduced the polynomial distributed
lags model, she suggested that endpoint constraints always
be employed. The endpoint constraints put explicit restric-
tions on the distributed lag weights outside of their rele-
vant range and also imply homogeneous restrictions on the
lag weights inside the range via homogeneous restrictions on
the polynomial coefficients. The problem is that endpoint
constraints have no basis in economic or econometric theory
as Schmidt and Waud (1973) had pointed out. As a result,
they represent a set of ad hoc restrictions whose sole
purpose is to increase the efficiency of estimation. Taking
^ For the discussion, see the study by Yohe and Karnosky (1969).
84
this problem of endpoint constraints into consideration,
there was no economic justification for using them and thus
the weights in this study were estimated without endpoint
constraints.
Also a combination-of-criteria-approach was used for
the selection of the lag length and the degree of the poly-
nomial. The selection was based on R-Square in conjunction
with the residual variance criterion, the size of the t-val-
ues of the estimated parameters, and in addition the cri-
terion that the model does not contradict conventional eco-
nomic wisdom.
Theoretically, it is generally agreed that following a
ter a lag and are preceded by the liquidity and first phase
loanable-funds effect. Also the income effect lags rather
than leads the liquidity effect. Thus a model with entirely
positive coefficients of the estimate has a theoretical flaw
since the liquidity effect is absent.
For this reason the selection problem was not handled
only by statistical procedures. As is often cautioned, the
analyst may be convinced on a priori grounds that one
specification is more realistic than another, in which case
he should be justified in applying the former even if the
latter has a slightly smaller residual variance or a higher
R-Square.
85
10
Other Procedures
The sample observation for this study were time series
and though it may appear advantageous to maximize the de-
grees of freedom by lengthening the series, the basic struc-
ture that the model seeks to explain may have undergone im-
portant changes. And if the structure had undergone any
changes, the true coefficients for the different structures
likely would have been different and thus coefficients esti-
mated using a unified sample would not have been reliable.
The Chow test was the basic procedure used to test for
any structural divergence in the model within any given sam-
ple period. Details of the Chow test and other relevant
considerations are presented below.
-^ For a complete coverage of this topic, see Henri Theil (1971). See also Thomas H. Wannacott and Ronald J. Wannacott (1977, pp. 375).
We conclude once again that statistical theory alone does not provide absolutely firm guidelines for accepting the null hypothesis; acceptance must be based also on extrastatistical judgement. Thus prior belief plays a key role, not only in the initial specifications of which regressors should be in the equation, but also in the decision about which ones should be dropped in light of statistical evidence, as well as in the decision on how the model eventually will be used.
86
Brief Outline of the Chow Test
The test has the following major steps:
(a) Using the sample observations, obtain the ordinary
least squares estimates from the entire sample. Us-
ing these estimates, calculate the sum of squared
residuals; ^^2 ^p ^ j (Y - Y ^ t t 1=1 o p
where Yo = actual value,
Yp = estimated value,
and T = Sample size.
The sum of squared residuals has T-K degrees of
freedom, where K is the nuraber of parameters esti-
mated.
(b) Two separate subsaraples are then obtained from the
entire sample corresponding to the two different
structures hypothesized. Again obtain ordinary
least squares estimates from each subsaraple using
two regressions and calculate the sum of squared
residuals for each subsaraple; jru & ju tl t2
(c) Next calculate ^^*2 ^ ^^2_ (zû ^ + 211 2)
Then calculate the F-ratio
"*2 J:U^ /
F =
C U i + Û 2 / (T - 2K)
87
(d) Finally look up the table F-value for K and T-2K
degrees of freedom at the chosen level of signifi-
cance. If the calculated F-value is less than the
table F-value, then the two structures are the same
at the given level of significance. And the struc-
tures are different if the calculated F-value exceed
the table F-value.
To double check results obtained, the dummy variable
test, that advanced by Damodar Gujarati, was in every case
applied over the same period accepted or rejected for struc-
tural stability by the Chow test. Moreover the dummy vari-
able test was a very efficient method using the SHAZAM-'--'-
program with respect to time as the F-test value could be
obtained directly from the computer print-out, thus elimi-
nating manual calculations as with the Chow test. Whenever
there was any conflict in the two procedures (there were
only two instances and both of them with United Kingdora
data), the structure with a longer time period was selected.
•^•^ SHAZAM (Solomon, Hercules, Atlas, Zeus, Achilles, Mercu-ry) is an econometric computer program developed by Kenneth J. White now of University of British Columbia, Vancouver-Canada. Developraent of SHAZAM was began by White in 1969 at Rice University, Houston, Texas and is now available at over 180 coraputer installations in 26 countries. For a complete coverage of the SHAZAM program see Kenneth J. White, UBC SHAZAM--An Econometric Computer Program, UBC computing cen-ter, 1980.
88
Brief Outline of the Dummy Variable
Test
Let us suppose that we want to study the relation be-
tween consumption (C) and income (Y) for two set of observa-
tions Nl, and N2. Let us also assurae that consuraption and
income are linearly related as follows:
C = p + sY
To use the dummy variable technique to test for equali-
ty between the sets of coefficients for the two linear re-
gressions, introduce the dummy variable in the additive and
the multiplicative forms as follows:
C = p + rD + sY + (tDY) + U
where D = 1 if the observation lies in the
first set (Nl observations).
D = 0 if the observation lies in the sec-
ond set (N2 observations).
The coefficients r and s are differential intercept and
differential slope coefficients, respectively. If r is sta-
tistically significant, the intercept value of the first set
is obtained by p + r, p in this case being the intercept
value of the second set. If r is statistically insignifi-
cant, p then gives an estiraate of the common intercept term
of both sets. If t is statistically significant, the slope value of the first set is s + t, s being the slope value of
89
the second set in this situation. If t is statistically
insignificant, s gives the slope value which is common to
both sets. Thus with the help of the additive and multipli-
cative duramies we can tell whether two linear regressions
differ either in the intercept or the slope or both.
Therefore there are certain advantages to the duraray
variable technique over the Chow technique. First, in just
one regression we can obtain all the information we need,
whereas the Chow test is a multi-stage procedure. Second,
if two regressions are different the Chow test will show
that they are different without, however, specifying the
source(s) of the difference, that is whether the difference
is due to the intercept or the slope or both. The dummy
variable method, on the other hand, clearly points out the
source(s) of difference.
And the final procedure was a static forecast and a
static simulation of the rate of change in the interest rate
given a monetary disturbance. First in-sample static simu-
lations, followed by out-of-sample forecasts were made with
the fundamental purpose of measuring the predictive perform-
ances of the models within the sample period as well as
out-of-the saraple period.
For quarterly observations the forecast and simulation
were done using estimated parameters of the raodel covering
90
the entire period belonging to the same structure. However,
because of extremely low R-Squares for monthly observations
when longer time periods were used, forecast and simulation
with monthly data was for the period 1978-1980 and only on
SAMl.
CHAPTER V
RESULTS AND ANALYSIS
The results of the test on the structure for each time
series of the monetary aggregates are presented first, along
with an analysis of the implications of these results on
earlier studies spanning longer periods, and possible expla-
nations or reasons of the breaks in the structures. Then
the empirical estimations of the main equation are present-
ed, followed by a discussion of the meaning of the coeffi-
cients, analysis and any iraplications from these results as
well as comparisons with past studies.
Segmentation of Time Period
United States
Adjusted Monthly Observations
The Chow test showed that at the 5 percent level of
significance, there was evidence of a stable structure from
1965-1980 for Ml, whereas for the much broader monetary ag-
gregates, M2, M3, and L there was evidence of a stable
structure from 1960-1980, implying that the 1959 data group
was an outlier. The sarae tirae periods were retested using
the dummy variable test and in each instance the same
results were obtained as can be seen from Table 1.
91
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94
Key to Table Notations and Defini-tions of Variables
* Null hypothesis accepted at the 1 percent significance
level.
Null hypothesis rejected even at the .001 percent sig-
nificance level.
*** Null hypothesis accepted even at the 25 percent signif-
icance level.
SAMl = Seasonally adjusted Ml.
SAM2 = Seasonally adjusted M2.
SAM3 = Seasonally adjusted M3.
SAL = Seasonally adjusted L.
UAMl = Seasonally unadjusted Ml.
UAM2 = Seasonally unadjusted M2.
UAM3 = Seasonally unadjusted M3.
UAL = Seasonally unadjusted L.
Q-Name implies a quarterly observation of the variable
rather than a monthly. For instance Q-SAMl is the quarterly
observation of the seasonally adjusted Ml.
Seasonally Unadjusted Monthly Observat ions
With seasonally unadjusted data, there was evidence of
a stable structure for Ml frora 1960-1980 with the 1959 data
being an outlier. However, for the broader defined monetary
aggregates (Ml, M2, M3, and L) a stable structure ran from
95
1959-1980. Again the dummy variable test confirmed each of
the results obtained using the Chow test.
Quarterly Observations
The null hypothesis of a stable structure for the en-
tire sample period 1959-1980 was accepted for all quarterly
time series of the monetary aggregates, both seasonally and
seasonally unadjusted, with one exception, Ml. For Ml there
was evidence of a stable structure from 1960-1980 as is evi-
denced from Table 1.
United Kingdora
Seasonally Adjusted Monthly Obser-vations
The Chow test in the case of the United Kingdom showed
evidence of a stable structure going from January 1972 to
December 1980 for Ml and M2, whereas for M3 a stable struc-
ture went from June 1971 - December 1980. However, the dura-
ray variable test indicated a stable structure going frora
January 1973 - December 1980 for both Ml and M2, while giv-
ing identical results for M3. These results are presented
in Table 2.
96
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Seasonally Unadjusted Monthly Ob-servations
For the seasonally unadjusted data, both the Chow test
and the dummy variable test showed evidence of a stable
structure running through out the entire period of available
monthly series, which is September 1971 to 1980 for Ml, July
1971-1980 for M2 and June 1971-1980 for M3.
Quarterly Observations
For all the monetary aggregates, seasonally as well as
seasonally unadjusted, both tests showed evidence of a sta-
ble structure going from I/1969-IV/1980, as can be seen from
Table 2.
Federal Republic of Germany
Seasonally Adjusted Monthly Obser-vations
With the Federal Republic of Germany, there was evi-
dence of a stable structure for the entire sample period,
1969-1980, for all the monetary aggregates when both tests
were applied. The null hypothesis that the structure is
stable was accepted for each monetary aggregates even at the
25 percent significance level as is evidenced in Table 3.
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ô'
cj îQ a
f s i
101
Seasonally Unadjusted Monthly Ob-servations
Both tests showed evidence of a stable structure run-
ning from 1960-1980 for Ml with the 1959 data being an out-
lier; from 1961 to 1980 for M2 with the 1959 and 1960 data
being outliers, and 1969-1980 for M3 which is also the en-
tire sample period of available data.
Quarterly Observations
Again as with the United Kingdom, there was evidence
with German data of a stable structure running throughout
the sample period when both tests were applied to all the
monetary aggregates, both seasonally and seasonally unad-
justed.
Possible Explanations for the Structural Divergence
When broadly considered, there appeared to be evidence
of a structural break in the late 1950's or early 1960's for
both the United States and the Federal Republic of Germany.
As can be seen from Table 4, the divergence of the structure
in the early 1960's may have been brought about by the
drastic increase in the level of nominal interest rates and
the inflation rate. The increase in the inflation rate may
have led to the development of inflationary expectations,
102
+ •
TABLE 4
Average Annual Growth Rate of Ml, and Inflation Rate, and Short-Term Treasury bill Rate
UNITED STATES I I
1 1954-1966 1967-1982 I
^ ^
Ml growth 2.47% 6.37% I
Inflation rate 2.19 6.49 I I I
Treasury bill rate 2.86 7.20 I I +
FEDERAL REPUBLIC OF GERMANY I I +
1960-1966 1973-1980 I I 1
Ml growth 7.51% 8.7% | I I
Inflation rate 3.29 4.7 | I I
Treasury bill rate 2.91 4.40 I
which eventually lowered the time lag of interest rates ad-
justment to any monetary disturbance. The major cause of
inflation from early 1960 to early 1980 in the United States
had been the stimulus to total spending provided by an
excessive rate of expansion in the money stock. For
instance, from early 1965 to the end of 1968 the money
103
stock, on balance, grew at a 5.2 percent annual rate,
compared with a 2 percent trend rate in the 1950's.
This change in structure in the 1960's from this study,
confirmed an earlier conclusion by Klein (1975). Klein ar-
gued that there was a fundamental change in the character of
the monetary system since World War II, that before World
War II and to a lesser extend to the end of World War II,
the United States and United Kingdom were regarded as being
on specie standards. However, in post World War II and par-
ticularly in the 1960's the monetary system is completely
fiduciary.
Of course the rapid growth in the money stock accompa-
nied by accelerating inflation was understandable. But a
rapid expansion of the money stock accompanied by high and
rising nominal interest rates has appeared a paradox to many
observers, since according to modern Keynesian economic
theory, an acceleration in the rate of monetary expansion
will provide lower interest rates (see Table 4). However,
Irving Fisher around the turn of the century developed an
economic theory which provided an explanation for this ap-
parent paradox when Fisher hypothesized that nominal
interest rate is made up of two components--the "real" rate
of interest, and a premium based on expected changes in the
price level.
104
For the United Kingdom, broadly speaking, there
appeared to be a structural divergence after 1971, specifi-
cally on the seasonally adjusted narrowly defined money
stock. Also analogous to the United States experience in
the early 1960's, accelerating inflation was experienced in
the United Kingdom following the nonconvertability of the
dollar into gold as ordered by President Richard Nixon in
August 1971, with a historic high reached in 1975 of 24.2
percent annual rate.
Moreover British prices increased more rapidly than
those in any other industrial country between 1972-1977 as
is evidenced from Table 5.
Empirica1 Estimation Results
Table 6 through Table 28 presents estimates using equa-
tion (3) for the various monetary aggregates of the three
countries. For each monetary aggregate the regression esti-
mation was carried out within the time period that a stable
structure existed.
The format of the presentation will be as follows:
Monthly observations for the United States will be presented
first, followed by quarterly observation estimates. Then a
similar presentation will be made for the United Kingdom,
followed by West Germany.
105
TABLE 5
Annual Rate of Change in Money and Prices in Six Industrial Nations 1971-1977
Changes in Money (M) and Prices (P) (Annual Rate of Percentage Change) I ^
U.S CANADA JAPAN F.R.G FRANCE U.K
M 6.2 27.8 29.7 12.8 11.9 15.3 1971
P 4.3 2.9 6.3 5.3 5.5 9.4 + ^ M 7.6 15.5 24.7 13.9 14.9 15.9
1972 P 3.3 4.8 4.8 5.5 5.9 7.1
I ^ M 7.3 13.8 16.7 .7 9.8 5.1
1973 P 6.2 7.6 11.8 6.9 7.3 9.1
4 ^ M 2.8 11.7 11.5 12.2 15.2 10.8
1974 P 11.6 10.9 22.7 7.0 13.6 15.9
I 1 M 4.4 7.8 10.3 14.1 10.5 15.0
1975 P 9.2 10.8 12.0 5.9 10.2 24.2
I 1 M 5.0 6.2 14.3 10.4 12.2 14.6
1976 P 5.7 7.6 9.3 4.6 8.8 16.8
I + M 7.5 7.2 7.0 8.3 13.6 13.5
1977 P 6.5 8.0 8.0 3.9 6.4 15.9
106
United States
Monthly Observations
Estimation Results for Ml Seasonal-ly Adjusted 1965-1980-Seasonally Unadjusted 1960-1980
Table 6 presents estimation results for the United
States monthly monetary aggregate for Ml.-'- The regression
estimates for the seasonally adjusted observations covers
the time series 1965-1980 since, as can be seen from Table
1, this is the period for which there was a stable structure
in the relationship. On the other hand, the seasonally
unadjusted estimation of the equation was from 1960-1980,
which is also a time period for which there was a stable
structure in the time series.
The "best" fit for the seasonally adjusted Ml, was a
sixth-degree polynomial with a distributed lag length of 24
months, while the "best" fit for the seasonally unadjusted
1 Barten-R-Square is the coefficient of determination esti-mated using a procedure outlined by A. P. Barten. For a complete description and derivation of the Barten-R-Square, see A. P. Barten (1962).
D-W is the Durbin Watson h statistic for autocorrela-tion. For a complete description and determination of this statistic, see Durbin, James and G. Watson (1950).
VNR is the Von Neumann Ratio of autocorrelation. For a complete description, see Von Neumann John (1941).
RHOl is the autocorrelation coefficient estimation of Hatanaka. For a full discussion of this statistic, see Mi-chio Hatanaka (974).
107
+
+
TABLE 6
United States Monthly Regression Results for Ml-'-
Const aO al a2 a3 a4 a5 a6 a7 a8 a9 alO all al2 al3 al4 al5 al6 al7 al8 al9 a20 a21 a22 a23 a24
Const. aO al a2 a3 a4 a5 a6 a7 a8 a9 alO all al2 al3 al4
1960-
Coeff.
-0.161 1.317 1.844 1.438 0.716 0.337
-0.024 -0.090 0.305 0.612 0.474 0.427 0.609
-0.301 -1.308 -1.107
Unadjusted -1980
t
-1.56 3.16 4.48 3.65 2.62 1.26
-0.09 -0.34 1.17 2.31 1.80 0.27 2.17
-0.75 -3.49 -3.83
Sum of Lag Coeffs. 29 Lag Length 24 Mean lag 6 Degree of Polynom. 6 R2 0 Barten-R' 0 D-W 1 RHOl 0
097
484
37 33 55 22
5 14 1 12 0 0 1 0
249
19
17 13 33 33
+
+
108
I TABLE 6 (Continued) I I +
VNR 1.56 1.34 I SER 0.065 0.004 I
I + I
Note: Units of the coefficients are in basis pointsl per 1 percentage point change in the monthly I annualized rate of growth of the money stock.I
Ml was a twelfth-degree polynomial with a lag length of 14
months. The mean lag for the seasonally adjusted Ml was
6.48 months and 1.19 months for the seasonally unadjusted
Ml.
The mean or average lag is the time that elapses until
half of the effect of a change in the independent variable
is reflected in the dependent variable. It is simply the
weighted-average lag, where the estimated coefficients are
used for the weights. When all of the weights are positive,
the formula for the mean lag is simply a weighted sum divid-
ed by the sum of the weights, but when negative coefficients
are mixed with positive coefficients, the formula is a lit-
tle more complicated.
A mean lag of 6.48 months for adjusted Ml implies that
half of the total effect of a change in the growth rate of
the adjusted money stock, Ml, is reflected on interest rates
after approximately 6 months. For the seasonally
unadjusted Ml, half the effect of the change in the growth
109
rate of the money stock is reflected in interest rates after
inly 1.20 months.
The results in both cases are consistent with a contem-
poraneous liquidity and first phase loanable-funds effects.
The coefficient of the contemporaneous change in the growth
rate of the money stock is negative (-0.14 for seasonally
adjusted Ml, -0.16 for the seasonally unadjusted Ml) and
significant for the seasonally adjusted data but insignifi-
cant for the seasonally unadjusted data. As expected, the
combined liquidity and first phase loanable-funds effect is
only temporary and quite small. This finding supports the
hypothesis of the model and also gives support to earlier
findings by Brown and Santoni (1983) and Hoehn James (1983),
and to the theoretical argument by Friedman (1968a, 1968b)
and Michael Darby (1975).
However, the R-Square, which measures the proportion of
the variation in the interest rate "explained" by the re-
gression is low, especially for the adjusted data. It is 37
percent for the seasonally adjusted Ml, and a mere 17 per-
cent for the unadjusted data. Also the Durbin Watson h sta-
tistic was low in each case, an indication that there may be
some serial correlation of the error terms.^ But more
^ However, a close look at most empirical results in the literature showed that most of them had very low R-Square for the monthly observations whenever the time period used
110
important was the fact that the sums of the coefficients on
Ml growth rate are significantly different from zero and po-
sitive in each case (29.10 basis points for adjusted Ml and
5.20 basis points for unadjusted Ml).
The sum over the coefficients of 29.10 and 5.20 basis
points for adjusted and unadjusted Ml respectively implies
that if the growth rate of Ml were to increase by 1 percent
and continue increasing at this rate, ceteris paribus, then
after 24 months, interest rate levels would have risen by
0.29 percent above the level before the start of the in-
crease in the growth rate of Ml, if the increase was on ad-
justed Ml. However, if the increase was on unadjusted Ml,
then interest rate levels would have risen by 0.05 percent
after 14 months.
Estimation Results for M2 Seasonal-ly_ Adjusted 1960-1980--Seasonally Unadjusted 1959-1980
Table 7 presents regression results for M2. The struc-
tural relationship was stable from 1960-1980 for adjusted
data, and 1959-1980 for unadjusted data and hence the esti-
mation was done over these periods. The lag length was
was moderately long (Cagan, 1972; Gibson, 1970a). This may be an indication that there is no long-run stable relationship between a change in the money growth rate and the nominal interest rate when only monthly observations are considered.
Mean lag 18.323 22.991 I Degree of Polynom. 6 5 I R^ 0.87 0.71 I Barten-R^ 0.81 0.59 I D-W 2.953 2.641 I RHOl -0.482 -0.446 I VNR 3.164 2.829 I SER 0.0763 0.1077 I
4 1
Note: Units of the coefficients are in basis pointsl per 1 percentage point change in the quarterlyl annualized rate of growth of the money stock.I
coefficients of lag 49 through lag 72 have negative signs
for the adjusted data, while coefficients of lag 54 through
72 also have negative signs. These negative coefficients
towards the end of the structure may be residuals from the
lag structure due to overshooting and undershooting. Brown
and Santoni (1983) aiso had end-of-structure negative coef-
ficients on their 1954-1970 estimation of the relationship
between changes in money growth and changes in interest
rates for U.S. monthly data. Of course without any restric-
tions placed on the coefficients, there is no particular
reason to expect them to be a smooth function of the lag.
The sum of the coefficients on monetary growth change
are again significantly different from zero and positive.
The sum of the coefficients is 20522.0 basis points and
5036.0 basis points for adjusted and unadjusted quarterly Ml
120
respectively. The iraplication here is that if the rate of
growth of adjusted quarterly Ml were to increase by 1 per-
cent and keep increasing at that rate, with all other things
held constant, then interest rates level would have risen by
205 percent after an 18 year period (72 quarters). This
means that interest rates will go up at an average rate of
11.34 percent every year or 3.80 percent every quarter.
Similarly if the increase is on unadjusted quarterly Ml,
then interest rates would have risen by 50.4 percent after
72 quarters, a 2.8 percent average annual rate or a 0.69
percent average quarterly rate.
The coefficients of determination for these estimations
were much higher than those for the monthly observations, 87
percent for the adjusted Ml and 71 percent for the seasonal-
ly unadjusted Ml. There was no evidence of any serial cor-
relation of the error terms as the Durbin Watson h statis-
Sum of Lag Coeffs. 38.927 39.269 Lag Length 60 60 Mean lag 27.100 27.662 Degree of Polynom. 2 2 R2 0.25 0.24 Barten-R^ 0.20 0.20 D-W 1.947 1.891 RHOl 0.026 0.050 VNR 1.986 1.931 SER 0.0912 0.0913
Note: Units of the coefficients are in basis points per 1 percentage point change in the monthly annualized rate of growth of the money stock.
r
133
The results obtained here followed a really textbook
pattern, a contemporaneous and temporary negative liquidity
and first phase loanable-funds effect, followed by positive
coefficients all the way to the end of the structure. All
but 3 of the coefficients of the adjusted data were signifi-
cant as were all but 4 coefficients for the unadjusted data.
However, the coefficients of determination were not high,
but there was no evidence of any serial correlation of the
error terms,
The lag length was 60 months with a polynomial of sec-
ond degree for the adjusted data, while the lag length was
also 60 months with a polynomial of second degree for the
unadjusted data. The mean lag for both series were approxi-
mately 27 months. The sum of the coefficients on Ml growth
rate were both positive, 38.93 basis points for adjusted
data (0.08 percent average rise annually), and 39.37 basis
points for unadjusted data (also 0.08 percent average rise
annually in interest rates if money growth rate is increas-
ing at one percentage point monthly).
Estimation Results for M2
Table 15 presents the regression results for M2. The
estimation was over the period January 1972 - December 1980
for adjusted data and September 1971 - December 1980 for
unadjusted data. The lag length was 9 months with a polyno-
Sum of Lag Coeffs. 28.793 1.990 I Lag Length 78 10 I Mean lag 28.36 0.76 I Degree of Polyno 2 6 I R^ 0.30 0.12 I Barten-R^ 0.24 0.07 I D-W 1.658 1.830 I RHOl 0.152 0.085 I VNR 1.705 1.848 I SER 0.06 0.09 I
I 1 I
Note: Units of the coefficients are in basis pointsl per 1 percentage point change in the monthly I annualized rate of growth of the money stock.|
Quarterly Observations
The United Kingdom estimation results for quarterly ob-
servations are presented in tables 17-19 (pp. 140-146).
Also as in the case of the United States, the results are
virtually identical to the monthly results and again with
the coefficients of determination for the quarterly results
also being significantly higher.
Estimation Results for Quarterly Ml
For quarterly observations, the time span of availabil-
ity of data is much longer. Thus the estimation period for
Mean lag 30.330 11.042 I Degree of Polynom. 6 2 I R^ 0.62 0.03 I Barten-R^ 0.58 0.02 I D-W 2.53 2.27 I RHOl -0.27 -0.13 I VNR 2.57 2.28 I SER 0.0599 0.0883 4
Note: Units of the coefficients are in basis pointsl per 1 percentage point change in the monthly I annualized rate of growth of the money stock.I
Estimation Results for M3 1969-1980
Table 22 presents estimation results for M3. Estima-
tions were carried out over the period 1969-1980. The
length of the lags were 72 months for both series and the
degree of polynomial was tenth for adjusted M3 and fifth for
unadjusted M3. The mean lags were 38.35 and 31.86 months
respectively. There was neither a contemporaneous liquidity
nor a first phase loanable-funds effect for both series.
The sum of the lagged effects were negative, -103.23 basis
points for adjusted M3 and -46.04 basis points for unadjust-
I a77 - 39.2 -3.16 I a78 - 30,4 -3.01 I ^ I I Sum of Lag Coeffs. -14.080 85853 I Lag Length 24 78 I Mean lag 12.280 36.102 I Degree of Polynom. 9 6 I R^ 0.90 0.98 I Barten-R^ 0.83 0.84 I D-W 2.763 3.467 I RHOl 0.382 0.747 I VNR 2.883 3.900 I SER 0.0497 0.0392 I 1 I I Note: Units of the coefficients are in basis points I per 1 percentage point change in the quarterly I annualized rate of growth of the money stock.
Estimation Results for Quarterly M3 I/1969-IV/1980
Estimation results for quarterly M3 are presented in
Table 25. The lags length are 36 quarters for adjusted and
unadjusted M3. The degree of polynomials are third and sec-
ond respectively. The mean lags are 18.75 and 21.65 quar-
ters, respectively.
There is a temporary and contemporaneous negative
effect in both time series. The seasonally unadjusted M3
coefficients followed a textbook pattern. The adjusted M3
coefficients had negative signs from lag 20 through 36. The
sum of coefficients on M3 growth rate is positive in both
Sum of Lag Coeffs. 185.54 143.26 Lag Length 36 36 Mean lag 18.75 21.649 Degree of Polynom. 3 2 R2 0.81 0.70 Barten-R^ 0.74 0.57 D-W 2.547 3.475 RHOl 0.299 0.762 VNR 2.779 3.971 SER 0.0613 0.0695
I + Note: Units of the coefficients are in basis points
per 1 percentage point change in the quarterly annualized rate of growth of the money stock.
cases, 185.54 basis points for adjusted M3 and 143.26 basis
points for unadjusted M3.
Revised Estimation of Equation on SAMl 1978-1980
Because of the low coefficients of determination for
monthly observations whenever estimation was carried out
over a moderately long time period, re-estimation was car-
ried out on seasonally adjusted Ml (see Tables 26-28) for
167
l .
l .
1 t
TABLE 26
United Kingdom Regression Result
Const. aO al a2 a3 a4 a5 a6 a7 a8 a9 alO all al2 al3 al4 al5 al6 al7 al8 al9 a20
Note: Units of the coefficients are in basis pointsl per 1 percentage point change in the monthly I annualized rate of growth of the money stock.l
and Fisher effect was again highest for the United States,
2585.2 basis points, and lowest for the United Kingdom,
39.831 basis points. The Durbin-Watson h statistics didn't
give any indication of autocorrelation for any of the three
countries.
Simulation Results
Tables 29-31 presents full in-sample and out-of-sample
simulations summary statistics for monthly observations of
SAMl for the three countries, using estimated coefficients
for the period 1978-1980. Avoiding the problem of ending-up
with excessive number of tables, results presented here, and
later with the quarterly models, are only for seasonally ad-
justed narrowly defined money, Ml.
^ The Mean-Square error of forecast is the average of the sum of the squared deviations of the predicted values from the observed values of the variable concerned. And the Root-Mean-Squared Error (RMSE) is the square root of the
172
TABLE 29
United States Full In-Sample Simulation And Post-Sample Forecast Summary Statistics On Monthly
SAMl 1978-1980
Sum of Absolute Errors Mean Error Sum of Squared Errors Mean Squared Error Mean Absolute Error Root Mean Squared Error Theil Inequality Coeff, U
United Kingdom Full In-Sample Simulation And Post-Sample Forecast Summary Statistics On Monthly
SAMl 1978-1980
+ + In-Sample Out-Of-Sample 1978-1980 1981-1983
I 1 Sum of Absolute Errors 0.30075 6.86340 Mean Error 0.00056 -0.04433 Sum of Squared Errors 0.00855 1.94430 Mean Squared Error 0.00057 0.05555 Mean Absolute Error 0.02005 0.19610 Root Mean Squared Error 0.02387 0.23569 Theil Inequality Coeff, U 0.308 3.084
173
TABLE 31 I I
West Germany Full In-Sample Simulation And Post-Sample I Forecast Summary Statistics On Monthly SAMl 1978-1980 I
I I
I ^ In-Sample Out-Of-Sample I 1978-1980 1981-1983 I
\- t Sum of Absolute Errors 0.33608 106.9100 Mean Error -0.01919 0.9307 Sum of Squared Errors 0.06307 531.9300 Mean Squared Error 0.00485 17,7310 Mean Absolute Error 0.02585 3.5638 Root Mean Squared Error 0.06965 4.2108 Theil Inequality Coeff, U 0.111 15.866
Full in-sample simulations and post-sample forecasts
summary statistics of quarterly observations on SAMl models
mean-squared error. Thus the smaller the RMSE of forecast, the better the forecast.
The Theil Inequality Coefficient, U, is the ratio of the RMSE divided by the square root of the mean sc uare successive difference of the observed values. U is equal 0, if and only if the forecasts are all perfect. Also U=l when the prediction procedure leads to the same RMSE as the naive no-change extrapolation. In other words, by using the inequality coefficient one measures the seriousness of a prediction error by the quadratic loss criterion in such a way that the zero corresponds with perfection and the unit with the loss associated with no-change extrapolation, The coefficient ranges from zero to infinity, which means it is possible to do considerably worse than by extrapolating on no-change basis. For a complete description of the derivation and interpretation of the the Theil coefficient, see Henri Theil (1966).
174
are presented on tables 32-34.
TABLE 32
United States Full In-Sample Simulation And Post-Sample Forecast Sumraary Statistics On Quarterly
SAMl
I + In-Saraple Out-Of-Sample 1969-1980 1981-1983
I + Sum of Absolute Errors 0.61202 65.2320 Mean Error -0.84D-12 -5.4360 Sum of Squared Errors 0.40798 516.3300 Mean Squared Error 0.002720 43.0280 Mean Absolute Error 0.04080 5.4360 Root Mean Squared Error 0.05215 6.5596 Theil Inequality Coeff, U 0.269 40.1320
The various models all showed evidence of a far better per-
formance within the sample period than beyond the sample.
The Theil inequality coefficient was less than one in every
instant within the sample period and so was the root mean
squared error. On the other hand, both the Theil coeffi-
cient and the root mean square were far greater than one in
most instances beyond the sample period. There was a
general trend of under-prediction beyond the sample period;
this may have been due to the excessively high and rising
nominal interest rates in the 1980's with a historic high in
175
TABLE 33
United Kingdom Full In-Sample Simulation And Post-Sample Forecast Summary Statistics On Quarterly
SAMl
+ ^ In-Sample Out-Of-Sample I 1969-1980 1981-1983 I + 1
Sum of Absolute Errors 0.11423 0.90735 I Mean Error 0.00102 0.03035 I Sum of Squared Errors 0.00330 0.12738 I Mean Squared Error 0.00066 0.01158 I Mean Absolute Error 0.02285 0.08249 I Root Mean Squared Error 0.02285 0.10761 I Theil Inequality Coeff, U 0.431 0.771 |
TABLE 34
West Germany Full In-Sample Simulation And Post-Sample Forecast Summary Statistics On Quarterly SAMl
+ + I In-Sample Out-Of-Saraple I 1978-1980 1981-1983 + •
Sum of Absolute Errors 0.48761 16.62900 Mean Error 0.00171 1.66290 Sum of Squared Errors 0.02171 39.88100 Mean Squared Error 0.00136 3.98810 Mean Absolute Error 0.03048 1.66290 Root Mean Squared Error 0.03683 1.99700 Theil Inequality Coeff, U 0.452 17.617
X
1-76
the short-term U.S. Treasury bill of 16.30 percent in May
1981, of 16.18 in March 1980 in the United Kingdom, and of
7.28 in 1981 and 1982 in West Germany.
This quotation highlights the feelings about the level
of interest rates in the 1980's.
The Administration may choose to hide its head, Ostrich-like, in the warm sand of economic dogma, but the rest of us must face facts. We cannot tolerate these sky-high interest rates—rates that until recently would have been considered usuri-ous. Congress must act to bring down these killer rates before they bring down our economy and the strength and security of our nation (Congressional Record-Senate, 1982, S699-700).
Also many other real factors besides a monetary disturbance
affect the movement of nominal interest rates and these fac-
tors are assumed-away within the sample period, since the
model coefficients are estimated without them. However,
this was not an isolated incident, as there are similar
problems of predicting interest rates movement beyond the
sample period in the literature. Another major cause could
be the high volatility of the change in the growth rate of
the money stock within this period.
For monthly SAMl forecasts, the percentage of the RMSE
of forecast to the RMSE that would have been observed if the
forecaster had confined himself to a naive no-change
extrapolation for the in-sample, was 22 for the United
States, 31 for the United Kindom, and 11 for the Federal
Republic of Gerraany. This is an indication that the German
177
model for the monthly data from 1978-1980 had the best
performance as regards predictive power, Beyond the sample
period, the percentage was 6047 for the United States, 308
for the United Kingdom and 1587 for West Germany. Thus the
United Kingdom's model predictive perforraance was best be-
yond the saraple period. The United States' model predictive
performance was the poorest beyond the sample period, and
the United Kingdom's model predictive performance was the
poorest within the sample period.
Also for the quarterly data, it was better predicting
than extrapolating on a no-change basis within the sample
period for all three countries. However, one did considera-
bly worse by predicting than extrapolating on a no-change
basis beyond the sample period for the United States and
West Germany. For the United Kingdom one did better by pre-
dicting both within and beyond the sample period. The Unit-
ed States model's predictive performance was the best within
the sample period, however it was again the poorest beyond
the saraple period. Possible explanations for the corapara-
tively poor perforraance of United States' raodels beyond the
saraple period are:
1. More rapid financial innovations have taken place in
the United States than in the other two countries
corabined.
178
2. The volatility in the change of the growth rate of
the money stock has been far higher in the United
States than in any of the other two countries.
3. Norainal interest rates in the United States are to a
much greater extent deterrained by market forces than
by any coercion on the part of the Treasury.
4. Also there has been a more rapid deregulation of the
banking industries in the United States in the past
three years than in the other countries.
CHAPTER VI
SUMMARY AND CONCLUSION
Most economies in the world have been experiencing high
levels of inflation during the past decade. At the same
time nominal interest rates have risen to extremely high
levels in these same countries, The worldwide inflation has
been attributed to several factors such as; the growth of
the Eurodollar, the loss of confidence in money, the float-
ing exchange rate system, and finally the tenfold increase
in the price of oil. Rapid growth of the raoney stock accom-
panied by high and rising nominal interest rates has ap-
peared a paradox to raany.
In the simple classroom raodel, there is a negative re-
lationship between changes in the money supply and interest
rates, as an increase in money supply implies that rates
should fall, and a decrease implies that rates should rise.
This notion is based on the theory of liquidity preference,
which models an individual desire to hold liquid assets--us-
ually taken to consist entirely of raoney. In this raodel, an
increase in the supply of raoney causes the araount supplied
to exceed the amount demanded. Thus individuals attempt to
reallocate their portfolios toward raarkets with determined
yields. However, with a fixed supply of these assets,
demand is now greater than supply, which causes the prices
179
180
of these assets to rise, or interest rates to fall, in order
to clear the market, As a result of the drop in interest
rates on these alternative assets, individuals are willing
to hold a larger amount of money.
The simple Keynesian implied inverse relation between
changes in the quantity of money and interest rates, was
widely taken for granted until as recently as the
mid-1960's, But by now it has been almost discredited by
simultaneous upward trends of the past several decades in
the quantity of money, nominal income, inflation, and inter-
est rates,
Is this recent observation inconsistent with the liq-
uidity preference theory? The answer to this question is no.
The liquidity preference function or effect still implies a
negative relationship between money and interest rates. The
theoretical and empirical argument is that, this liquidity
effect is not permanent, it is a temporary effect that dis-
sipates rapidly given efficient financial and capital mar-
kets,
This argument, first raised by Milton Friedman (1968a),
and other follow-ups were in reaction to the emergence in
the advanced countries of accelerating raoney growth and
rising interest rates that made it impossible to continue to
regard a stable or permanent Keynesian liquidity preference
function relating the nominal quantity of money inversely to
181
the nominal interest rates as an adequate tool for analyzing
the effect of monetary changes on interest rates. Empirical
work in this regard were largely along the lines pioneered
by Irving Fisher, Most of the earlier studies largely con-
firmed Fisher's results, particularly his conclusion that
inflationary expectations were formed on the basis of a long
past period and only slowly adjust to experience. This con-
clusion was the basis for his interpretation of the Gibson
paradox, the long observed positive correlation between in-
terest rates and the level of prices. However, recent stud-
ies tend to suggest that the period of experience on which
expectation are based has shortened drastically after the
mid-1960's
The raajor goal of this study was to further test for
the existence of a stable liquidity preference runction us-
ing the raost recent data, extending the analysis to cover
more than two countries, deriving models for all the mone-
tary aggregates frora Ml to L with both seasonally and sea-
sonally unadjusted data, and finally covering quarterly in
addition to monthly observations. The initial sample was to
be 1959-1980 with 1981-1983 data used for the measurement of
the predictive performance of the models beyond the period
of study, However, some of the estiraation periods were
actually shorter due to nonavailablity of data for some
182
countries and also due to the nonexistence of a stable
structure throughout this period in raany cases.
The analysis was carried out using an Almon polynomial
distributed lag. This procedure was chosen because of its
inherent advantages over other procedures such as the ordi-
nary least square. Some of these advantages are its flexi-
bility and the nonexistence of the problem of multicolli-
nearity and also the high frequency of its use in the
literature. The Chow and dummy variable tests were used in
determining the periods of stable structure within the sam-
ple period,
Suraraary of Results
The tirae spans of stable structures were different for
the different countries and monetary aggregates. Even for
the same monetary aggregate, the structures were sensitive
to the seasonality as well as the aggregation of the data.
Thus the sarae monetary aggregate sometiraes exhibited one
tirae span of a stable structure for the raonthly data and a
different one for the quarterly data.
Also the models did not seem to fit any particular
polynomial or lag length. The polynoraials and lag lengths
were random for each country. Regarding monthly data, we
found a positive relationship between the rate of change of
183
the money stock and interest rates for all the monetary
aggregates in the case of the United States. For instance,
the results for the seasonally adjusted Ml in Table 6 indi-
cate that the total effect on the rate of growth of interest
rates due to a change in the growth rate of the money stock
is 29.047 less 0.141, giving a net effect of 28.956. Thus
if the monthly rate of growth of the money stock were to in-
crease by one percent and to continue increasing at that
rate, then interest rates would have risen by 28.9 basis
points after 24 months or in a two-year period, everything
else staying constant. Half the net effect would have been
realized (the mean lag) after 6.48 raonths, a little over one
half of a year.
In the case of the United Kingdom, we also found a po-
sitive relationship for all the monetary aggregates. For
example, frora the seasonally adjusted Ml result in Table 14,
the net effect was 38.485, after a sixty-raonth lag, iraplying
that interest rate would have risen by 38.39 basis points
after 5 years if the raonthly growth rate of the raoney stock
were to increase by one percent and continue growing at that
rate for 5 years, with all other things constant.
With the Federal Republic of Germany, we had mixed
results for the monthly aggregates. There was a positive
relationship for Ml and a negative one for M2 and M3.
184
For all three countries, and for all the monetary
aggregates, with the exception of West Gerraan M2 and M3,
there was a conteraporaneous liquidity effect which was neg-
ative as expected. The coefficient of this contemporaneous
change in the growth rate of money was not only negative,
but it was quite small in raost cases and only teraporary.
However, with the coefficients of determination for
these raonthly models very low, re-estimation was carried out
for the 1978-1980 period on seasonally adjusted Ml for all
the three countries. For each country, we found a positive
relationship and a liquidity effect which is not perraanent.
In this short period, the net effect in the case of the
United Kingdora was virtually unchanged, 39.528 (see Table
27) but the net effect for the United States and West Germa-
ny increased to 2585.70 and 791.36 respectively. The coef-
ficients of determination were relatively higher and there
was no indication of any autocorrelation problera.
Regarding quarterly data, the results were virtually
identical to the monthly results, but with relatively higher
coefficients of determination. Again a positive relation-
ship was found for all quarterly monetary measures, with the
exception of West German M2 and M3. With quarterly data the
effects persisted for much longer lags and the net effects
were also much greater. For instance, the net effect for
seasonally adjusted Ml, was 20192 (see Table 10) after a 72
185
quarters (18 years) lag for the United States, 167.92 (see
Table 17) after 40 quarters (10 years) lag for the United
Kingdom and 406.491 (see Table 23) after 30 quarters (7.5
years) for West Germany. The raean lags were 18.323 quarters
for the United States, 38.346 for the United Kingdom, and
14.864 for the Federal Republic of Germany.
The raodels performed very well as regards prediction
within the sample period; both the root mean square error
and the Theil inequality coefficient were less than one in
every case. However, the performances of the models' pre-
dictions were not as good beyond the sample period, as the
Theil inequality coefficients were in every case greater
than one. But none of the root mean square errors exceeded
a value of 7.0.
Conclusion
Results of this study largely support Brown and Santo-
ni's conclusion less than a year ago that, in the United
States for the period 1971-1980, there was a positive rela-
tionship between the nominal interest rate and the money
supply. However, their conclusion was arrived at only on
the basis of estiraation of the seasonally adjusted raonthly
Ml. But this study indicates that this relationship is true
frora the early-1960's to 1980 and not only for the
186
seasonally adjusted Ml but also for the broader raonetary
aggregates, seasonally as well as seasonally unadjusted
data. Thus these results broadly suggest that an increase
(decrease) in the raonetary growth rate that persists for
more than one month or one quarter will give rise to an in-
crease (decrease) in interest rates, ceteris paribus, for
the United States. These results are also consistent with
estimations by Jaraes G. Hoehn (1983, p. 8), when he re-
gressed the first difference of the log of the federal funds
rate on the distributed lag first difference of the log of
Ml money stock. He reported positive sum of Ml growth coef-
ficients. Results also give evidence of the sarae conclusion
for the United Kingdora, with both monthly and quarterly
data. However, no simple generalization could be raade in
the case of West Gerraan results, since results indicated a
positive relationship for Ml and a negative relationship for
M2 and M3.
The findings here are also consistent with Gibson and
Cagan's earlier conclusion. Gibson's (1970b, p. 298) empir-
ical estiraations showed that
changes in the rate of monetary change have immediate and significant negative effect on market interest rates. However, following this negative effect, adjustments in the rate of income increase and soon begin to exert pressure to return interest rates to their original level, three to nine months after the rate of raonetary increased was changed.
187
Cagan (1972, p. 103) on the other hand concluded that
an increase in the monetary growth rate in stage t has a negative effect on interest rates in stage t, zero effect in stage t+1, and positive effects thereafter.
However, the findings from our study are not consistent with
Gibson's conclusion, with regard to the period of interest
rates returning to their original level. After the 1960's,
interest rates returned to their original level much faster
(in less than three raonths in most cases); and this view is
supported by Yohe and Karnosky's findings which concluded
that price level changes since 1952 have evidently come to
have a prompt and substantial effect on price expectations
and norainal interest rates.
These results also suggest that some earlier studies
that have carried out estimation over very long periods, may
have the problem of coefficients being estimated over peri-
ods belonging to different structures and thus were not true
c.oef f icients. For exaraple, Gibson (1970b) carried out a
study of the relation between interest rates, and current
and past rates of change of money growth, monthly observa-
tions within the period 1947-1966. If the redefinition of
Ml has not changed the data so rauch, then the estimations
for this study were done across two different structures as
there is evidence of a structural break in the early 196 's.
Also Cagan's (1972) study which covered the period
188
1910-1965, regressing the commercial paper rate on lagged
values of monetary growth rate, may have a sirailar problem
unless the redefinition of the monetary aggregate Ml did
change the data structure substantially. And our period of
structural divergence, broadly speaking for the United
States and United Kingdom, corresponds to those of sorae ear-
lier studies. Klein (1975) reported that there was a funda-
raental change in the character of the monetary system since
World War II, and that the United States and the United
Kingdom have changed from being on specie standards before
World War II, to being on a fiduciary raonetary systera in
post World War II, particularly in th 1960's. Also Kajal
(1976) concluded that his calculations supported earlier
findings by Gibson and Turnovsky that both the interest rate
equation and the expectations forraation equation had a
structural break around 1960, when he used the distributed
lag, the extrapolative, and the Frenkel expectation hypothe-
sis. Yohe and Karnosky (1969) also found that the total ef-
fect of price expectations on interest rates and the speed
at which they are formed appeared to have increased since
1960.
Even though this study has failed to be conclusive for
all the monetary aggregates of all the countries in the
study, it at least suggests that a conclusive assertion can
be raade on the narrowly defined raonetary aggregate Ml
189
(seasonally as well as seasonally unadjusted, and raonthly as
well as quarterly aggregated data) of all the three coun-
tries. And the assertion is that the liquidity function is
not a stable or perraanent effect and that the direction and
magnitude of the change in short-term interest rates will
mirror the change in monetary growth. This is consistent
with some earlier studies with similar results. For exam-
ple, Brown and Santoni (1983) deraonstrated that data for the
raost recent period reveal a statistically significant but
economically anemic liquidity effect that dissipates rapid-
ly. This was to be expected, given efficient financial and
capital markets.
Because of time and budget constraints, only three
countries were covered in this study. Besides the number of
countries, there are also other limitations to this re-
search. Other nonraonetary factors affecting the level of
interest rates in the economy were not incorporated into the
models. These nonraonetary variables such as the government
budget deficit or surplus, and the level of economic activi-
ty (either an expansionary stage or a recessionary stage)
obviously do influence the deraand for credit by both the
governraent and the private sector. For instance the
magnitude of the budget deficit and its effect on the level
of interest rates as well as other economic variables has
190
been a major concern in the United States Congress and in
the financial communities both inside and outside the United
States in recent months, especially in countries such as
Mexico, Argentina, and Brazil which are under huge debts to
banks in the United States.
For these reasons, it is suggested that further inves-
tigations be done covering other countries and the nonmone-
tary factors affecting the level of interest rates in the
economy should be incorporated into the models before any
specific complete generalizations can be raade.
Despite these shortcomings, this study's major contri-
bution to the literature is the fact that the findings here
with recent data and across three countries, give support to
both the theoretical arguments and the empirical estimations
which showed that a stable or permanent liquidity preference
function relating the norainal quantity of raoney inversely to
the nominal interest rates is an inadequate tool for analyz-
ing the effect of monetary changes on interest rates.
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APPENDICES
A, Sources of Data for the Monetary Stock Measures and
the Treasury Bill Rate
B, Data of Monetary Stock Measures and the 3-Month
Treasury Bill Rate for the United States
C. Data of Monetary Stock Measures and the 3-Month
Treasury Bill Rate for the United Kingdom
D. Data of Monetary Stock Measures and the Equivalent
of the 3-Month Treasury Bill Rate for the Federal
Republic of Gerraany
iOO
APPENDIX A
SOURCES OF DATA FOR THE MONETARY MEASURES AND THE TREASURY BILL RATE
(1) Bank of England's Quarterly Bulletin, Statistical Annex,
(2) Federal Reserve Board of Governors Publishing Depart-
raent, Washington D, C.
(3) Federal Reserve Bulletin.
(4) International Econoraic Conditions, Federal Reserve Bank
of St, Louis,
(5) Monthly Report of the Deutsche Bundesbank, Statistical
Section.
(6) Organization For Econoraic Co-operation and Development
Financial Statistics Monthly.
(7) Organisation For Economic Co-operation and Developraent